Browse Function problems Studdy Solved!

Problem 6301

The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to the area where your computer indicated the communication device was stored. You look past the gate hopefully, as your computer translates: The passcode for this gate is found by determining the domain of the derivative of $f(x)$ and then evaluating the derivative at $x=-\frac{12}{38}$ . Enter the domain in interval notation. $f(x)=\sqrt{4-38 x}$
Domain of $f^{\prime}(x)$ : $\square$ 固朝 $\hat{a}^{b}$ $\sin (a)$ $\infty$ $\alpha$ $f^{\prime}\left(-\frac{12}{38}\right)$ $\square$
Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.

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Problem 6302

How much money must you invest now at $4.1 \%$ interest compounded continuously in order to have $\$ 10,000$ at the end of 4 years?
You must invest \\square$ (Round to the nearest cent as needed.)

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Problem 6303

Use the graph of the function to answer the question. (s) 2017 StrongMind. Created using GeoGebra.
What is the output of the function when the input is 0 ? Enter your answer as a number, like this: 42

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Problem 6304

13. A function $f(x)$ is one-to-one. If the graph of $f^{-1}(x)$ lies in the fourth quadrant. In which quadrant does the graph of $f(x)$ lie? A. First Quadrant B. Second Quadrant b) Given the graph of the function $h(x)$ . graph $h^{-1}(x)$ C. Third Quadrant D. Fourth Quadrant

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Problem 6305

Let $A(t)=4000 e^{0.06 t}$ be the balance in a savings account after $t$ years. Complete parts (a) through (f) below. (a) How much money was originally deposited?
There was $\$$ $\square$ originally deposited. (Type an integer or a decimal.)

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Problem 6306

Let $A(t)=4000 e^{0.06 t}$ be the balance in a savings account after $t$ years. Complete parts (a) through (f) below. (a) How much money was originally deposited?
There was \$ 4000 originally deposited. (Type an integer or a decimal.) (b) What is the interest rate?
The interest rate is $\square \%$ . (Type an integer or a decimal.)

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Problem 6307

Four thousand dollars is deposited into a savings account at $4.5 \%$ interest compounded continuously. (a) What is the formula for $A(t)$ , the balance after $t$ years? (b) What differential equation is satisfied by $A(t)$ , the balance after $t$ years? (c) How much money will be in the account after 9 years? (d) When will the balance reach $\$ 8000$ ? (e) How fast is the balance growing when it reaches $\$ 8000$ ? (c) $\$ 5997.21$ (Round to the nearest cent as needed.) (d) After $\square$ years the balance will reach $\$ 8000$ . (Round to one decimal place as needed.)

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Problem 6308

Examine the input-output table, which contains some of the ordered pairs of a linear function. \begin{tabular}{|c|c|} \hline Input $(x)$ & Output $(y)$ \\ \hline-4 & 4 \\ \hline-2 & 1 \\ \hline 0 & -2 \\ \hline 4 & -5 \\ \hline \end{tabular}
What is the initial value of the function? $-4$ $-2$ 0 4

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Problem 6309

The Eighth Gate Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this gate for me." Your computer replies with the follow: The function $f(t)=a\left(\sin \left(t^{6}\right)\right)^{10}$ models the position of an oscillating particle that has recently been discovered. Assume that $a$ is a constant. What is the function that represents the velocity of this particle?
Note: If you want to write a power of a trigonometric function, remember that writing $\sin (\mathrm{x})$ to the fourth power as $\sin ^{4}(x)$ is just a shorthand method. To be mathematically correct, you should write that as $(\sin (x))^{4}$ . which is what your computer expects and can translate.
Velocity Function: $\square$ $a^{b}$ $\sin (a)$ $\infty$ $\alpha$ $\square$ Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.

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Problem 6310

Find $d u$ and $u$ \begin{tabular}{|l|} \hline 6. $\int \operatorname{Arctan} x d x$ \\ \hline 7. $\int \frac{\operatorname{Arcsin} 2 x d x}{\sqrt{1-4 x^{2}}}$ \\ \hline 8. $\int x \csc \left(1-x^{2}\right) \cot \left(1-x^{2}\right) d x$ \\ \hline 9. $\int 10^{\cos x} e^{\cos x} \sin x d x$ \\ \hline $10 \int x^{3} e^{2 x} d x$ \\ \hline \end{tabular}

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Problem 6311

1. Find the minimum value of $2 x^{2}+12 x+4$ and the value/values of $x$ where the minimum is attained.

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Problem 6312

$\int t e^{4 t} d t$

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Problem 6313

$\int \cos ^{4} \theta \sin ^{3} \theta d \theta$

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Problem 6314

$\int_{1}^{4} \frac{5 x+1}{\sqrt{x^{3}}} d x$

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Problem 6315

6.0 Sulla base delle informazioni che puoi dedurre dal grafico, completa le uguaglianze seguenti. a. $\lim _{x \rightarrow-\infty} f(x)=$ $\qquad$ f. $\lim _{x \rightarrow-\infty} \frac{1}{f(x)}=$ . $\qquad$ b. $\lim _{x \rightarrow-1^{-}} f(x)=$ $\qquad$ g. $\lim _{x \rightarrow-2^{+}} \frac{1}{f(x)}=$ $\qquad$ D] $-\infty$ c. $\lim _{x \rightarrow 1^{+}} f(x)=$ $\qquad$ d. $\lim _{x \rightarrow+\infty} f(x)=$ $\qquad$ h. $\lim _{x \rightarrow 1^{-}} e^{f(x)}=$ $\qquad$ e. $\lim _{x \rightarrow 0}[f(x)+3]=$ $\qquad$ i. $\lim _{x \rightarrow 1^{+}} e^{f(x)}=$ $\qquad$

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Problem 6316

To find the intervals of increase and decrease, as well as the points of extrema for the function $F(x) = x + \frac{6}{(-8x+4)^{1/2}}$ , we need to:
1. Determine the first derivative $F'(x)$ .
2. Find the critical points by setting $F'(x) = 0$ and solving for $x$ .
3. Use the first derivative test to determine the intervals of increase and decrease.
4. Identify the points of local maxima and minima based on the sign changes of $F'(x)$ .
Given the second derivative $f^{\prime\prime}(x) = \frac{20-x}{2 \sqrt{-2x+1}(-2x+1)^2}$ , we can also analyze the concavity and possible inflection points.

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Problem 6317

ما قيبة $\lim _{x \rightarrow-3} \frac{x^{3}+27}{x^{2}+4 x+3}=$
اخترأحد الذيارات $\frac{2}{27}$ $\frac{-27}{2}$ $\frac{27}{2}$ $\frac{-2}{27}$

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Problem 6318

إذا كانت $\lim _{x \rightarrow 1}\left(\frac{f(x)-f(1)}{x-1}\right)=10 \text { ركت } f(x)=m x^{2}$
فإن قيمة m تساوي اخترأحد الخيارات a. 2 b. 5 c. 3 d. 1

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Problem 6319

10.1 Given $f(x)=3-x^{2}$ (with domain $\left.(-\infty, \infty)\right)$ , $g(x)=2-x($ with domain $(-\infty, \infty))$ , $h(x)=\frac{1}{x}$ (with domain $\left.(0, \infty)\right)$ , find the following compositions (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ h$ (d) $g \circ h$ (+) hof; What is the domain this function? $(+)$ hog; What is the domain this function? 10.2 Determine the inverses of the following functions (a) $f(x)=4-5 x$ , (with domain $(-\infty, \infty)$ ) (b) $h(x)=x^{2}-3 x+2$ , (with domain $\left.\left.(2, \infty)\right)\right]$ $(+) f(x)=\frac{2 x+1}{3-x}$ , (also find the domain and range of $\ell$ and of $f^{-1}$ )

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Problem 6320

Let $f(x)=-3 x+4$ . Then $f^{-1}(x)=$

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Problem 6321

البطة نات الفاصلة 0 انظر الميكل المقبل . - $f^{\prime}(-2)$ ） $f(0)$ ( 0 $\lim _{h^{\prime} \rightarrow 0} \frac{f(-1+h)-f(-1)}{h}$ . $f(x)=-x^{3}-3 x^{2}+2$

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Problem 6322

The Sugar Sweet Company is going to transport its sugar to market. It will cost $\$ 4500$ to rent trucks plus $\$ 225$ for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function. $C(n)=4500+225 n$
Answer the following questions. (a) If the total cost is $\$ 9900$ , how many tons is the company transporting? $\square$ ns (b) What is the total cost of transporting 12 tons? \\square$

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Problem 6323

The Sugar Sweet Company is going to transport its sugar to market. It will cost $\$ 4500$ to rent trucks plus $\$ 225$ for each ton of sugar transported. The total cost, $C$ (in dollars), for transporting $n$ tons is given by the following function. $C(n)=4500+225 n$
Answer the following questions. (a) If the total cost is $\$ 9900$ , how many tons is the company transporting? $\square$ tons (b) What is the total cost of transporting 12 tons? \$7200

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Problem 6324

Given $f(x)=3 x+9$ a) Evaluate $f(5)$ $f(5)=$ $\square$ b) Evaluate $f(-4)$ $f(-4)=$ $\square$ Question Help: $\square$ Message instructor

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Problem 6325

Suppose that a company's profit (in terms of $x$ , the number of units sold) is given by the model $P(x)=-4 x^{2}+221 x-650$ . Find the profit when 23 units are sold.
Answer: $\square$ dollars. Question Help: Message instructor Submit Question

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Problem 6326

Graph $y=\frac{5}{3} x-9$

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Problem 6327

Find the domain of the function $f(x)$ . $f(x)=\frac{4}{5 x-9}$
Select the correct choice below and, if necessary, fill in the answer box to complete you A. The domain is $\{x \mid$ $\square$ \}. (Simplify your answer. Type an inequality or a compound inequality.) B. The domain is $\square$ 3. (Simplify your answer. Use a comma to separate answers as needed.) C. The domain is $\{x \mid x$ is a real number and $x \neq$ $\square$ \}. (Simplify your answer. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers.

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Problem 6328

27) Find the function of $g(x)$ by using function $f(x)$ . A) $g(x)=-f(x-3)+2$ B) $g(x)=-f(x+3)+6$ C) $g(x)=-f(3-x)+2$ D) $g(x)=-f(x-3)+6$

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Problem 6329

3. A certain mass hangs from a spring above a table. It is released from a height of 0.9 metres above the table and falls to a height of 0.1 m above the table before reversing direction and bouncing back to 0.9 m . The mass continues to move in a periodic up and down motion. It takes 1.2 seconds for the mass to return to the same position each time. b) Write an equation which expresses the height $h$ as a function of $\sin \theta$ .

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Problem 6330

Evaluate the indicated function for $f(x)=x^{2}+2$ and $g(x)=x-3$ $\begin{array}{c} (f+g)(2) \\ (f+g)(2)= \end{array}$ Submit Answer

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Problem 6331

1. a. Express $\cos (x)$ in terms of $\cot (x)$ and $\csc (x)$ . b. Express $\csc (x)$ in terms of $\cos (x)$ and $\tan (x)$ .

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Problem 6332

nomework11.4: Problem 1 (1 point)
Compare and discuss the long-run behaviors of the functions below. In each blank, enter either the constant or the polynomial that the rational function behaves like as $x \rightarrow \pm \infty$ : $f(x)=\frac{x^{4}-7}{x^{3}-6}, g(x)=\frac{x^{3}-7}{x^{3}-6}$ , and $h(x)=\frac{x^{2}-7}{x^{3}-6}$ $f(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas) $g(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas) $h(x)$ will behave like the function $y=$ $\square$ as $x \rightarrow \pm \infty$ . help (formulas)
Note: You can earn partial credit on this problem.

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Problem 6333

15. Water whose temperature is at $100^{\circ} \mathrm{C}$ is left to cool in a room where the temperature is $30^{\circ} \mathrm{C}$ . After 2 minutes, the water temperature is $88^{\circ} \mathrm{C}$ . If the water temperature $T$ is a function of time $t$ given by $T=30+70 e^{k t}$ , find $k$ . Round your answer to the nearest hundredth.

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Problem 6334

覑 W Write a quadratic function with zeros 6 and 7. "新] Write your answer using the variable x and in standard form with a leading coefficient of 1 . $f(x)=$ $\square$ 2 3 4

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Problem 6335

[效, Write a quadratic function with zeros 7 and -4. [i]. Write your answer using the variable x and in standard form with a leading coefficient of 1. $g(x)=$ $\square$ 2 3 4

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Problem 6336

A one-to-one function is given. Write an equation for the inverse function. $\begin{array}{r} s(x)=\frac{2}{x+3} \\ s^{-1}(x)= \end{array}$ $\square$

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Problem 6337

Q. Let $f(z)=\left\{\begin{array}{ll}\frac{z^{3}}{z^{2}} & \text { if } z \neq 0 \\ 0 & \text { if } z=0\end{array}\right.$ (1) $f(z)$ is Continuous everywhere on $\mathbb{C}$ (2) the Gmplex derivativ $f^{\prime}(0)$ das notexis

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Problem 6338

Part 1 of 4 (a) Show that $f(x)=3 x+3$ defines a one-to-one function.
A function is one-to-one if it can be shown that if $f(a)=f(b)$ , then $\square=\square$ . Assume $f(a)=f(b)$ .

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Problem 6339

(c) Estimate $\int_{0}^{4}\left(x^{2}+1\right) d x$ using a right-hand sum with $n=3$ (i.e. $\left.R_{3}\right)$ .
Round your answer to two decimal places. $R_{3}=$ $\square$

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Problem 6340

Part: $0 / 8$
Part 1 of 8 (a) Graph $f(x)=x^{2}-2 ; x \leq 0$ .

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Problem 6341

Question Evaluate the function $f(x)=3 \log (x+7)+2$ for $x=1$ . Round the final answer to the nearest two decimal places.

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Problem 6342

2. Describe the behavior of the function in words. A complete description would describe the initial value and would use descriptors such as "decays/grows by", "factor of," "\% growth/decay", etc. If the initial value was not specified in the article, make up a reasonable initial value and defend your choice. You are welcome to rescale the input (for example, time) at your convenience; if you do this just explain why you did it. Initial value is zero. The function describes exponential grouth. 100 deaths at day 0 . $600=a b^{t}$ $1900(1+r)^{t}$
3. Give an algebraic formula for the function, and define each of your variables with units. $\begin{array}{l} D(t)=D_{0}+b_{k G F}^{t} \\ D=\text { \#of deaths } t=\text { days }>1500=100 \cdot b^{15} \\ b^{15}=\frac{1500}{100}=15 \\ 6^{1 / 10} \approx 1.174 \\ 1,174^{15}=15 \end{array}$
4. Identify the growth factor and the growth or decay rate for the function. aproxmitly 1.174 , growth rate is about $17.4 \%$
5. Construct a table of values for the function. Include at least 5 sets of data points.
6. In your table, demonstrate where/how you can see the growth factor.

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Problem 6343

Part 1 of 9 (a) Graph $f(x)=\sqrt{x+3}$ .

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Problem 6344

Consider the following polynomial function. $f(x)=(x+1)(x-1)(x-3)$
Answer the questions regarding the graph of $f$ . Then, use this information to graph the function. (a) Choose the end behavior of the graph of $f$ .
Choose One (b) Ust each real zero of $f$ according to the behavior of the graph at the $X$ -axis near that zero. If there is more than one answer, separate them with commas. If there is no answer, click on "None",
Zero(s) where the graph crosses the $X_{\text {-axis: }}$ $\square$ Zero(s) where the graph touches, but does not cross the $X$ -axis: $\square$ (c) Find the $y$ -Intercept of the graph of $f$ : (d) Graph $f(x)=(x+1)(x-1)(x-3)$ by doing the following. - Plot all polnts where the graph of $f$ intersects the $x$ -axis or $y$ -axis. - For each polnt on the $\boldsymbol{X}$ -axis, select the correct behavior. - click on the graph icon.

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Problem 6345

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x-1)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}+2$ .

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Problem 6346

9 El diagrama muestra el gráfico de $y=2^{x}+3$ . La curva pasa por los puntos $\mathrm{A}(0, a)$ y $\mathrm{B}(1, b)$ . a Halle el valor de $a$ y el valor de $b$ . b Escriba la ecuación de la asíntota de la curva.

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Problem 6347

The following table gives the U.S. national debt for selected years from 1900 to 2013. \begin{tabular}{cccc} \hline Year & \begin{tabular}{c} U.S. Debt \\ (\ billions) \end{tabular} & Year & \begin{tabular}{c} U.S. Debt \\ (\$ billions) \end{tabular} \\ \hline 1900 & 1 & 1990 & 3233 \\ 1910 & 1 & 1996 & 5225 \\ 1920 & 24 & 2000 & 5674 \\ 1930 & 16 & 2005 & 7933 \\ 1940 & 43 & 2009 & 11,957 \\ 1945 & 259 & 2010 & 13,529 \\ 1955 & 273 & 2011 & 15,476 \\ 1965 & 314 & 2012 & 16,067 \\ 1975 & 533 & 2013 & 16,856 \\ 1985 & 1823 & & \\ \hline \end{tabular} (a) Using a function of the form y=a^{*} b^{\wedge} x $, with$ x=0 $in 1900 and$ y $equal to the national debt in billions, model the data. (Round your coefficients to four decimal places.)$ $y=0.9 \cdot 1.07^{x}$ $(b) Use the model to predict the debt in 2024. (Round your answer to the nearest billion.)$ $\$ 27.431$ \square $billion (c) Predict the year in which the debt will be$ \ $99$ trillion ( $\$ 99,000$ billion). $\square$ Need Help? Read It

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Problem 6348

Suppose functions $f$ and $g$ are defined as follows. \begin{tabular}{ccc} \hline $x$ & $f(x)$ & $g(x)$ \\ \hline 1 & 3 & 3 \\ 2 & 5 & 4 \\ 3 & 6 & 1 \\ 4 & 7 & 5 \\ 5 & 4 & 2 \\ \hline \end{tabular}
That is, $f(1)=3, g(1)=3, f(2)=5, g(2)=4$ , and so on. (a) Evaluate $f^{-1}$ (7). (2 Points)

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Problem 6349

$y=(4+x)^{-1 / 2}, \quad a=0$
Find the Linearization at $x=a$ . $L(x)=$

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Problem 6350

Homework 6: Problem 4 (1 point)
Find the linearization $L(x)$ of the function $g(x)=x f\left(x^{2}\right)$ at $x=2$ given the following information. $f(2)=0 \quad f^{\prime}(2)=6 \quad f(4)=3 \quad f^{\prime}(4)=-4$
Answer: $L(x)=$ $\square$

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Problem 6351

Write the domain in interval notation. $f(x)=\ln \left(x^{2}+9\right)$
The domain is $\square$

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Problem 6352

18 19 20 21 22 23 24 25 26 27
Write the domain in interval notation. Write your answers as integers or simplified fractions if necessary. $h(x)=\log _{2}(6 x+7)$
The domain is $\square$ . \begin{tabular}{ccc} \hline $\sqrt{\square}$ & $(\square, \square)$ & $\frac{\square}{\square}$ \\ { $[\square, \square]$ } & $(\square, \square]$ & { $[\square, \square)$ } \\ $\square \cup \square$ & $\infty$ & $-\infty$ \end{tabular}

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Problem 6353

The table shows the total personal income in the United States (in billions of dollars) for selected years from 1960 and projected to 2024. \begin{tabular}{cc|cc} \hline Year & Income (\ billions) & Year & Income (\$ billions) \\ \hline 1960 & 411.5 & 2008 & 12,100.7 \\ 1970 & 838.8 & 2014 & 14,728.6 \\ 1980 & 2307.9 & 2018 & 19,129.6 \\ 1990 & 4878.6 & 2024 & 22,685.1 \\ 2000 & 8429.7 & & \\ \hline \end{tabular} (a) These data can be modeled by an exponential function. Write the equation of this function, with x $as the number of years past 1960 and$ y $as the total$ $y=533.570 \cdot 1.065^{x} \quad \text { Way to gol }$ $ (b) Does the unrounded model overestimate or underestimate the total personal income given in the table for 2018? The model overestimates the projected total. The model underestimates the projected total.
Perfect (c) Graphically determine the year the model predicts total personal income will reach $\$ 31$ trillion. $\square$ Enter a number: Need Help? Read II Watch it

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Problem 6354

Which point is on the graph of $f(x)=3 \cdot 5^{x} ?$ A. $(1,15)$ B. $(15,1)$ C. $(0,0)$ D. $(0,15)$

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Problem 6355

Question Watch Video Show Examples
If $f(x)=x^{5}+5 x^{4}+4$ , then what is the remainder when $f(x)$ is divided by $x+3$ ?
Answer Attempt 1 out of 2

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Problem 6356

Composites Involving Exponential Functions Find the domain and range for each of the functions in Exercis 21-24.
21. $f(x)=\frac{1}{2+e^{x}}$
22. $g(t)=\cos \left(e^{-t}\right)$
23. $g(t)=\sqrt{1+3^{-t}}$
24. $f(x)=\frac{3}{1-e^{2 x}}$

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Problem 6357

```latex \begin{align} &\text{1-F: } [-1,8) \rightarrow \mathbb{R} \\ &F(x) = -2x - 5 \\ &\text{Fonk. İnceleyelim (Grafik, artanlık-azalanlık, max-min, Fonk. Sıfır., Fonksiyonun işareti)} \\ &F(x) = 2 \\ &f(x) \text{ örten} \end{align}

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Problem 6358

The marginal cost (in dollars per square foot) of installing $x$ square feet of kitchen countertop is given by $C^{\prime}(x)=x^{\frac{6}{7}}$ . a) Find the cost of installing $60 \mathrm{ft}^{2}$ of countertop. b) Find the cost of installing an extra $13 \mathrm{ft}^{2}$ of countertop after $60 \mathrm{ft}^{2}$ have already been installed. a) Set up the integral for the cost of installing $60 \mathrm{ft}^{2}$ of countertop. $C(60)=\int_{0}^{\square} \square \mathrm{dx}$

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Problem 6359

19 Die Verkaufszahlen (in 1000 Stück) einer neuen Schokolade werden durch die Funktion f mit $f(t)=4-4 \cdot e^{-0,1 t}$ beschrieben ( $t$ in Wochen). Berechnen Sie, wann die Verkaufszahlen innerhalb einer Woche um hundert Stück zunehmen.

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Problem 6360

In some South Asian weddings, the groom travels to the wedding on a white horse in a procession called a baraat.
A farm charges $\$ 1,000$ to rent a horse for a baraat, which includes transporting the horse up to 15 miles to the wedding. A $\$ 2.50$ fee applies for each mile beyond the first 15. An employee represents the situation with the function $C(m)=1,000+2.50 \mathrm{~m}$ and determines that the total cost to rent a horse for a wedding 25 miles away is $\$ 1,062.50$ .
Is the employee correct? Use the drop-down menus to explain.
Click the arrows to choose an answer from each monu. The function roprosonts the situation if $\boldsymbol{m}$ is tho Chooso... The employeo should substitute chooso... $\square$ for $m$ and determine that the cost to rent and transport tho horso is chooso... - Tho omployoo
Chooso... correct.

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Problem 6361

The student photo club at the college is planning on selling prints that it makes to raise money. The profit $P$ , in dollars, from selling $x$ prints is given by the function: $P(x)=217 x-2 x^{2}$ a) Find the number of prints, to the nearest whole print, that need to be sold to maximize the profit. You must sell $\square$ prints to maximize the profit. b) The maximum profit, to the nearest dollar, is $\$$ $\square$ . (No dollar signs or comma's.)

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Problem 6362

The diagram shows part of the graph of $y=a+b \sin x$ . Find the values of the constants $a$ and $b$ . $\qquad$ $\qquad$

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Problem 6363

homework4.8: Problem 4 (1 point)
Find an equation of the tangent line to the curve $x=\sin (5 t), \quad y=\sin (6 t)$ at $t=\pi$ . $\begin{array}{l} x(t)=\square \\ y(t)=\square \end{array}$ (Note that because the correctness of a parametrically described line depends on both $x(t)$ and $y(t)$ , both of your answers may be marked incorrect if there is an error in one of them.)
Note: You can earn partial credit on this problem. Preview My Answers Submit Answers

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Problem 6364

6) $[\mathrm{AC}](12) \mathrm{A}$ lab assistant sneaks into a grizzly bear's den during the winter months and hooks up a machine to monitor the bear's lung capacity in breathing. Luckily for the lab assistant, the bear is hibernating now. The lung capacity of the bear can be modelled by a sinusoidal function. a) Explain why the breathing of a hibernating grizzly bear can be modeled by a periodic function. b) Explain the meaning of the period in the context of this situation.

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Problem 6365

Find an equation of the tangent line to the curve $x=\sin (5 t), \quad y=\sin (6 t)$ at $t=\pi$ . $\begin{array}{l} x(t)=\mathcal{X} \\ y(t)=\square \end{array}$ (Note that because the correctness of a parametrically described line depends on both $x(t)$ and $y(t)$ , both of your answers may be marked incorrect if there is an error in one of them.)

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Problem 6366

$g(x)=-2 \cos \left(\frac{1}{3}\left(x+20^{\circ}\right)\right)+4$ e. State the equation of the axis of the curve f. State the amplitude g. State the period h. Does this sinusoidal function have a plase stifs to the lef or righte?

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Problem 6367

(25علا
اوجد $\frac{d y}{d x}$ للالدجراثات اليالية: $y=\frac{\tan (2 x)}{x^{2}+1}$

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Problem 6368

Anwendung: Die Flugbahn eines Papierfliegers wird durch folgende Funktionsgleichung beschrieben: $f(x)=-0,005 x^{2}+0,1 x+1,5$ a) Aus welcher Höhe wird abgeworfen? b) Wie weit geht der Wurf? 30 m 1,5 - c) Wie hoch fliegt der Flieger maximal? 2 m d) Fünf Meter hinter dem Abwurf steht eine 1,80 Hohe Mauer. Fliegt der Flieger über die Mauer? $\qquad$ -

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Problem 6369

\begin{align} 1) & \quad f(x) = 1 - 4x + x^5 \\ 2) & \quad f(x) = x^2 + 3 \\ 3) & \quad f(x) = 4 - x^2 \\ 4) & \quad f(x) = 2x^2 + 8x + 7 \\ 5) & \quad f(x) = -x^2 + 10x - 22 \\ 6) & \quad f(x) = 4x^2 + 24x \\ 7) & \quad f(x) = 6x - x^2 \\ \end{align}
Find the range of each function listed above.

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Problem 6370

In Exercises 41-46, describe how to transform the graph of $y=\ln x$ into the graph of the given function. Sketch the graph by hand and support your sketch with a grapher.
41. $f(x)=\ln (x+3)$
42. $f(x)=\ln (x)+2$
43. $f(x)=\ln (-x)+3$
44. $f(x)=\ln (-x)-2$
45. $f(x)=\ln (2-x)$
46. $f(x)=\ln (5-x)$

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Problem 6371

8 Gegeben ist die Funktion $f$ mit $f(x)=e^{2 x}$ a) Skizzieren Sie den Graphen von f.

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Problem 6372

An ice cube is freezing in such a way that the side length $s$ , in inches, is $s(t)=\frac{1}{2} t+4$ , where $t$ is in hours. The surface area of the ice cube is the function $A(s)=6 s^{2}$ . Part A: Write an equation that gives the volume at $t$ hours after freezing begins. ( 2 points) Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points) Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations, and check for extraneous solutions. (4 points)

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Problem 6373

Funktionenscharen: Sachaufgabe Der Damm Gegeben ist die Funktionenschar fa mit $f_{a}(x)=\frac{3 a x^{2}-x^{3}}{144} ; a>0$
Für bestimmte Werte von a beschreiben die Graphen von $f_{a}$ zwischen den Nullstellen von $f_{a}$ den Querschnitt eines Deiches. a Ermittle den Wert von a so, dass der Damm 15 m breit ist und hebe anschließend den entsprechenden Graphen in der rechten Abbildung farbig hervor. Beschrifte ihn korrekt. b Zeige, dass für a = 4 die Böschung auf der rechten Seite mit $45^{\circ}$ auf den horizontalen Boden trifft. c Ermittle den Wert von a so, dass der Deich an seiner höchsten Stelle 6 Meter hoch ist. [Kontrolle H (2a; $\frac{1}{36} \mathrm{a}^{3}$ )] d Wähle zwei verschiedene Werte für a und zeige, dass die Hochpunkte des entsprechenden Graphen von $f_{a}$ auf dem Graphen $G_{g}$ von $g$ mit $g(x)=\frac{1}{288} x^{3}$ liegen . e Bestimme die Stelle auf der linken Böschungsseite des Deiches, an der der Anstieg maximal wird (in Abhängigkeit von a).
Gib an, für welches a dieser maximale Anstieg $30^{\circ}$ beträgt.

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Problem 6374

Let F be the function below. If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more clearly.
Evaluate each of the following expressions. Note: Enter 'DNE' if the limit does not exist or is not defined. a) $\lim _{x \rightarrow-1^{-}} F(x)=$ $\square$ $\lim _{x \rightarrow-1^{+}} F(x)=$ $\square$ $\lim _{x \rightarrow-1} F(x)=$ $\square$ $F(-1)=$ $\square$ $\square$ b) $\lim _{x \rightarrow 1^{-}} F(x)=$ $\square$ $\lim _{x \rightarrow 1^{+}} F(x)=$ $\square$ $\lim _{x \rightarrow 1} F(x)=$ $\square$ $F(1)=$ $\square$ c) $\lim _{x \rightarrow 3^{-}} F(x)=$ $\square$ $\lim _{x \rightarrow 3^{+}} F(x)=$ $\square$ $\lim _{x \rightarrow 3} F(x)=$ $\square$ $F(3)=$ $\square$

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Problem 6375

Given the following functions, find each of the values: $\begin{array}{l} f(x)=x^{2}+6 x-7 \\ g(x)=x-1 \\ (f+g)(-3)= \\ (f-g)(1)= \\ (f \cdot g)(0)= \\ \left(\frac{f}{g}\right)(4)= \end{array}$

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Problem 6376

$S P u$ Q.13) If $f(x)=\frac{\sec x}{x+3}$ and $f^{-1}(c)=0$ , then $c=$ A. $\frac{1}{3}$ B. 0 C. $\frac{2}{\sqrt{3}}$ D. $\frac{1}{4}$ E.None

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Problem 6377

5 Q.13) If $f(x)=\frac{\sec x}{x+3}$ and $f^{-1}(c)=0$ , then $c=$ A. $\frac{1}{3}$ B. 0 C. $\frac{2}{\sqrt{3}}$ D. $\frac{1}{4}$ cibtifantstius orsil $2=$ Q.14) One of the following equations is symmetric about origin A. $y=\frac{x+1}{x}$ B. $-x^{5}+3 x$ C. $y=x^{4}-2 x^{2}+6$ D. None $\begin{aligned} -2= & \left.-x^{5}\right)^{3 x} \\ & -\left(x^{5}\right. \end{aligned}$ Q.15) One of the following functions is an even function A. $f(x)=\frac{\sec 4 x}{5 x}$ B.None C. $f(x)=\frac{\cos 5 x}{2 x}$ D. $f(x)=\frac{\sin 2 x}{3 x}$ Q.16)The range of the function $f(x)=\frac{1}{\sqrt{4-x^{2}}}$ is A. $(0,2)$ B. $[0,2]$ C. $\left(\frac{1}{2}, \infty\right)$ D. $\left[\frac{1}{2}, \infty\right)$ E.None Q.17) Given that $f(x)=\frac{1}{x-3}$ and $g(x)=\frac{1}{x}$ then the domain of the function $f \circ g$ is A. $R \backslash\left\{0, \frac{1}{3}\right\}$ $B . R \backslash\{0\}$ C. $R \backslash\left\{\frac{1}{3}\right\}$ D. $R \backslash\{0,3\}$ E.None Q.18) (The greatest integer less than or equals $x$ ) The range of $f(x)=2[x]$ is A. $\{0,61,62,63$ , $\qquad$ B. $R \backslash\{0,61,62,63$ $\qquad$ $f|x|$ sec - C. $\{0,62,64,66$ $\qquad$ D. $(-\infty, \infty)$ Q.19) If the domain of the function $y=f(x)$ is $[2,3)$ then the domain of $g(x)=f(3-x)$ is A. $[2,3)$ B. $(0,1]$ C. $[0,1)$ D. $(2,3]$ E.None Q.20) Given that $f(x)=\sec ^{-1} x$ then $f(2)=$ A. $\frac{1}{\sin 2}$ B. $\frac{1}{\cos 2}^{x}$ C. $\cos ^{-1}\left(\frac{1}{2}\right)$ D. $\sin ^{-1}\left(\frac{1}{2}\right)$ E.None Q.21) Given that $f(x)=x^{2}$ and $g(x)=\left\{\begin{array}{l}2 x, \\ x+3, x \geq 4\end{array}\right.$ then $\left.(f \circ g)(x)=f(x)\right)$ A. $\left\{\begin{array}{cl}4 x^{2} & , x<4 \\ (x+1)^{2} & , x \geq 4\end{array}\right.$ B. $\left\{\begin{array}{cl}4 x^{2} & , x \leq 4 \\ (x+1)^{2} & , x>4\end{array}\right.$ C. $\left\{\begin{array}{cc}4 x^{2} & , \quad x<16 \\ (x+1)^{2} & , \quad x \geq 16\end{array}\right.$ D. $\left\{\begin{array}{cc}4 x^{2} & , x \leq 16 \\ (x+1)^{2} & , x>16\end{array}\right.$ Q.22) The domain of the function $f(x)=\operatorname{Ln}(5-|7 x+3|)$ is A. $\left[-\frac{8}{7}, \frac{2}{7}\right]$ B. $\left(-\frac{8}{7}, \frac{2}{7}\right)$ C. $R \backslash\left[-\frac{8}{7}, \frac{2}{7}\right]$ D. $\mathrm{R} \backslash\left(-\frac{8}{7}, \frac{2}{7}\right)$ Q.23) The domain of $f(x)=\cos ^{-1}(3 x+1)$ is $-1,1$ $-24-$ ولا تعت:

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Problem 6378

Use product nule $f(x)=8 \sin x \cos x$

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Problem 6379

(9.) Function $q$ has domain $\{-3,-2.5,-2,-1.5,-1,-0.5\}$ and is defined by $q(x)=\frac{3}{x}$ . a. Complete the table. \begin{tabular}{c|c|c|c|c|c|c|} $\boldsymbol{x}$ & -3 & -2.5 & -2 & -1.5 & -1 & -0.5 \\ \hline $\boldsymbol{q}(\boldsymbol{x})$ & & & & & & \end{tabular} b. Graph q.

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Problem 6380

Find the range and the domain of the function shown.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.

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Problem 6381

Question \# 2: (Total 6 points, each 2 points) A) Let $f(x)=3 x^{4}-4 x^{3}-12 x^{2}+1$ . Find the absolute maximum and absolute minimum values of the function $f$ on the interval $[1,3]$ .

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Problem 6382

Find the function values given the function $k(x)=|x|+3$ . Complete parts (a) through (f) below. a) $k(0)=$ $\square$ (Simplify your answer.) b) $k(-5)=$ $\square$ (Simplify your answer.) c) $k(5)=$ $\square$ (Simplify your answer.) d) $k(-10)=$ $\square$ (Simplify your answer.) e) $k(a-3)=$ $\square$ (Simplify your answer.) f) $k(a+h)=$ $\square$ (Simplify your answer.)

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Problem 6383

خطوط التقارب 5
حدد كل خطوط التقارب الرأسية و المائلة للادالة a) $x=2, x=-3, y=x-1$ b) $x=2, x=-3, y=x+1$ c) $x=-2, x=-3, y=x-1$ d) $x=-2, x=3, y=x+1$

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Problem 6384

Question 1 (2 points) Use the Unit Circle to match the following cosine functions to their exact value.
1. 1
2. $-\frac{\sqrt{2}}{2}$ $\cos \left(90^{\circ}\right)$ $\cos \left(300^{\circ}\right)$ $\cos \left(390^{\circ}\right)$ $\cos \left(-120^{\circ}\right)$ $\cos \left(150^{\circ}\right)$
3. $\frac{\sqrt{2}}{2}$
4. -1
5. $\frac{1}{2}$
6. $-\frac{\sqrt{3}}{2}$
7. $\frac{\sqrt{3}}{2}$
8. 0
9. $-\frac{1}{2}$

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Problem 6385

homework4.8: Problem 6 (1 point)
Find parametric equations for the tangent line at $t=3$ for the motion of a particle given by $x(t)=8 t^{2}+7, y(t)=1 t^{3}$ . For the line, $\begin{array}{l} x(t)=\square \\ y(t)=\square \end{array}$ (Note that because the correctness of a parametrically described line depends on both $x(t)$ and $y(t)$ , both of your answers may be marked incorrect if there is an error in one of them.)
Note: You can earn partial credit on this problem.

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Problem 6386

3. Verify Mean-Value Theorem applies on the given interval, then find the values of $c$ in the interval that satisfy the conclusion: (Hint: Evaluate the slope of the secant line at the endpoints of the interval) $f(x)=x^{2}-x$ on the interval $[-3,5]$ .

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Problem 6387

Question 5 (1 point) The function below is a model that describes the cyclical variation of the price of a stock share as a function of time in months from January 2023 ( $t=0$ corresponds to January). $P(t)=1.5 \cos \left(\frac{\pi}{4} t\right)+3.5$
What is the highest price per share? $\square$ A
What is the lowest price per share? $\square$ A In what month is the price lowest? (Type the month, starting with a capital.) $\square$ A

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Problem 6388

In Exercises 41-46, describe how to transform the graph of $y=\ln x$ into the graph of the given function. Sketch the graph by hand and support your sketch with a grapher.
41. $f(x)=\ln (x+3)$
42. $f(x)=\ln (x)+2$
43. $f(x)=\ln (-x)+3$
44. $f(x)=\ln (-x)-2$
45. $f(x)=\ln (2-x)$
46. $f(x)=\ln (5-x)$

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Problem 6389

Below is the table for the function $f(x)$ . \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 3 & 6 & 7 & 13 & 14 \\ \hline $y$ & 1 & 5 & 8 & 10 & 15 \\ \hline \end{tabular}
Choose the one table below which is the inverse function $f^{-1}(x)$ .
\begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 14 & 13 & 7 & 6 & 3 \\ \hline $y$ & 15 & 10 & 8 & 5 & 1 \\ \hline \end{tabular}
\begin{tabular}{|r|r|r|r|r|r|} \hline $x$ & 3 & 6 & 7 & 13 & 14 \\ \hline $y$ & $1 / 1$ & $1 / 5$ & $1 / 8$ & $1 / 10$ & $1 / 15$ \\ \hline \end{tabular}
\begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 1 & 5 & 8 & 10 & 15 \\ \hline $y$ & 3 & 6 & 7 & 13 & 14 \\ \hline \end{tabular}
\begin{tabular}{|r|r|r|r|r|r|} \hline $x$ & $1 / 1$ & $1 / 5$ & $1 / 8$ & $1 / 10$ & $1 / 15$ \\ \hline $y$ & 1 & 5 & 8 & 10 & 15 \\ \hline \end{tabular}

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Problem 6390

(a) On a separate sheet of paper, sketch the parameterized curve $x=t \cos t, y=t \sin t$ for $0 \leq t \leq 4 \pi$ . Use your graph to complete the following statement:
At $t=4.5$ , a particle moving along the curve in the direction of increasing $t$ is moving down $\square$ and to the right (b) By calculating the position at $t=4.5$ and $t=4.51$ , estimate the speed at $t=4.5$ . speed $\approx$ $\square$ (c) Use derivatives to calculate the speed at $t=4.5$ and compare your answer to part (b). speed = $\square$
Note: You can earn partial credit on this problem. Preview My Answers Submit Answers

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Problem 6391

Problems that involve a regularly repeating pattern or oscillation can be modeled by trigonometric functions. A common example is using a trigonometric function to model blood pressure. Blood pressure measures the cyclic variation of pressure on the arterial wall as a response to heart rhythm.
The function below models the pressure cycle for one heartbeat. Pressure is measured in mm of mercury $(\mathrm{Hg})$ and time is measured in seconds. $P(t)=25 \sin \left(\frac{5 \pi}{2} t\right)+115$
The graph of $\mathrm{P}(\mathrm{t})$ is drawn above. Match the following features of the graph to their corresponding meanings. $\square$ Meaning of the period $\square$ $\qquad$ $\qquad$ $\qquad$ The amplitude of $\mathrm{P}(\mathrm{t})$ Meaning of the amplitude
The period of $\mathrm{P}(\mathrm{t})$ The blood pressure (systolic/diastolic) modeled by $\mathrm{P}(\mathrm{t})$
1. The change in blood pressure from the mean
2. The duration of one heartbeat (in seconds)
3. $140 / 90$
4. $4 / 5 \mathrm{sec}$
5. 25 mmHg
6. The maximum blood pressure
7. 115 mmHg
8. $115 / 25$
9. 48 bpm
10. 1.25 sec

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Problem 6392

Question 4 (1 point) The function below is a blood pressure model that describes a person's blood pressure in mm Hg as a function of time in seconds. $P(t)=15 \sin \left(\frac{13 \pi}{6} t\right)+110$
What is this person's heart rate in beats per minute? A bpm What is this person's maximum blood pressure? $\square$ $\underbrace{}_{\mathrm{mmHg}}$
What is this person's minimum blood pressure? $\square$ A) mmHg

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Problem 6393

What is the domain of the function shown in the table? \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 2 & 3 \\ \hline 4 & 4 \\ \hline 6 & 5 \\ \hline 8 & 6 \\ \hline \end{tabular} A. $(2,3),(4,4),(6,5),(8,6)$ B. $\{2,3,4,5,6,8\}$ C. $\{2,4,6,8\}$ D. $\{3,4,5,6\}$

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Problem 6394

Problems that involve a regularly repeating pattern or oscillation can be modeled by trigonometric functions. A common example is using a trigonometric function to model blood pressure. Blood pressure measures the cyclic variation of pressure on the arterial wall as a response to heart rhythm.
The function below models the pressure cycle for one heartbeat. Pressure is measured in mm of mercury $(\mathrm{Hg})$ and time is measured in seconds. $P(t)=25 \sin \left(\frac{5 \pi}{2} t\right)+115$
The graph of $\mathrm{P}(\mathrm{t})$ is drawn above. Match the following features of the graph to their corresponding meanings. $\square$ The period of $\mathrm{P}(\mathrm{t})$
1. The change in blood pressure from the mean Meaning of the period The blood pressure (systolic/diastolic)
2. The duration of one heartbeat (in seconds) modeled by $\mathrm{P}(\mathrm{t})$
3. $140 / 90$
4. $4 / 5 \mathrm{sec}$ The amplitude of $\mathrm{P}(\mathrm{t})$
5. 25 mmHg Meaning of the
6. The maximum blood pressure amplitude
7. 115 mmHg
8. $115 / 25$
9. 48 bpm
10. 1.25 sec

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Problem 6395

homework4.8: Problem 10 (1 point)
Find the length traced out along the parametric curve $x=\cos (5-2 t), y=\sin (5-2 t)$ as $t$ goes through the range $0 \leq t \leq 1$ . (Be sure you can explain why your answer is reasonable). arc length = $\square$
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Problem 6396

In Exercises $15-22$ , find $f(g(x))$ and $g(f(x))$ . State the domain of each.
15. $f(x)=3 x+2 ; g(x)=x-1$
16. $f(x)=x^{2}-1 ; g(x)=\frac{1}{x-1}$
17. $f(x)=x^{2}-2 ; g(x)=\sqrt{x+1}$
18. $f(x)=\frac{1}{x-1} ; g(x)=\sqrt{x}$
19. $f(x)=x^{2} ; g(x)=\sqrt{1-x^{2}}$
20. $f(x)=x^{3} ; g(x)=\sqrt[3]{1-x^{3}}$
21. $f(x)=\frac{1}{2 x} ; g(x)=\frac{1}{3 x}$
22. $f(x)=\frac{1}{x+1} ; g(x)=\frac{1}{x-1}$

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Problem 6397

Differentiate the function $f(t)$ with respect to $t$ , where $t = \frac{1}{(x-1)(x+3)}$ .

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Problem 6398

Question 6 (2 points) A hypertensive patient has a blood pressure of 140/100. The heart rate is 80 beats per minute. For this scenario, find a sine function of the form, $P(t)=a \sin (b t)+d$ where $P$ is the pressure in mm Hg and t is time in seconds. Note that there is no phase shift.
Enter the values of a, b, d as integers or decimals to the nearest tenth. You will need your calculator! $a=$ $\square$ A $b=$ $\square$ A $d=$ $\square$ A

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Problem 6399

The function below has the form $f(x)=b^{x}+d$ .
Which of the following functions is shown on the graph? $f(x)=2^{x}+6$ $f(x)=2^{x}+4$

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Problem 6400

The position of a body moving on a coordinate line is given by $s(t)=\frac{16}{t^{2}}-\frac{4}{t}$ for $1 \leq t \leq 4$ , with $s$ in meters and $t$ in seconds.
Note: You don't have to simplify the calculations; in other words, the problem will accept, for example, $3^{\star} 7 / 4$ . a. Find the body's displacement (change in position) and average velocity for the given time interval.
Displacement: $\square$ m
Average velocity: $\square$ $\mathrm{m} / \mathrm{s}$ b. Find the body's velocity at the endpoints of the interval.
Velocity at $t=1$ : $\square$ $\mathrm{m} / \mathrm{s}$
Velocity at $t=4$ : $\square$ $\mathrm{m} / \mathrm{s}$

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Function

Problem 6301

Problem 6302

How much money must you invest now at 4.1%4.1 \%4.1% interest compounded continuously in order to have $10,000\$ 10,000$10,000 at the end of 4 years?You must invest \ \square$ (Round to the nearest cent as needed.)

Problem 6303

Use the graph of the function to answer the question. (s) 2017 StrongMind. Created using GeoGebra.What is the output of the function when the input is 0 ? Enter your answer as a number, like this: 42

Problem 6304

Problem 6305

Let A(t)=4000e0.06tA(t)=4000 e^{0.06 t}A(t)=4000e0.06t be the balance in a savings account after ttt years. Complete parts (a) through (f) below. (a) How much money was originally deposited?There was $\$$ □\square□ originally deposited. (Type an integer or a decimal.)

Problem 6306

Problem 6307

Problem 6308

Problem 6309

Problem 6310

Problem 6311

1. Find the minimum value of 2x2+12x+42 x^{2}+12 x+42x2+12x+4 and the value/values of xxx where the minimum is attained.

Problem 6312

∫te4tdt\int t e^{4 t} d t∫te4tdt

Problem 6313

∫cos⁡4θsin⁡3θdθ\int \cos ^{4} \theta \sin ^{3} \theta d \theta∫cos4θsin3θdθ

Problem 6314

∫145x+1x3dx\int_{1}^{4} \frac{5 x+1}{\sqrt{x^{3}}} d x∫14​x3​5x+1​dx

Problem 6315

Problem 6316

Problem 6317

ما قيبة lim⁡x→−3x3+27x2+4x+3=\lim _{x \rightarrow-3} \frac{x^{3}+27}{x^{2}+4 x+3}=x→−3lim​x2+4x+3x3+27​=اخترأحد الذيارات 227\frac{2}{27}272​ −272\frac{-27}{2}2−27​ 272\frac{27}{2}227​ −227\frac{-2}{27}27−2​

Problem 6318

إذا كانت lim⁡x→1(f(x)−f(1)x−1)=10 ركت f(x)=mx2\lim _{x \rightarrow 1}\left(\frac{f(x)-f(1)}{x-1}\right)=10 \text { ركت } f(x)=m x^{2}x→1lim​(x−1f(x)−f(1)​)=10 ركت f(x)=mx2فإن قيمة m تساوي اخترأحد الخيارات a. 2 b. 5 c. 3 d. 1

Problem 6319

Problem 6320

Let f(x)=−3x+4f(x)=-3 x+4f(x)=−3x+4. Then f−1(x)=f^{-1}(x)=f−1(x)=

Problem 6321

Problem 6322

Problem 6323

Problem 6324

Given f(x)=3x+9f(x)=3 x+9f(x)=3x+9 a) Evaluate f(5)f(5)f(5) f(5)=f(5)=f(5)= □\square□ b) Evaluate f(−4)f(-4)f(−4) f(−4)=f(-4)=f(−4)= □\square□ Question Help: □\square□ Message instructor

Problem 6325

Suppose that a company's profit (in terms of xxx, the number of units sold) is given by the model P(x)=−4x2+221x−650P(x)=-4 x^{2}+221 x-650P(x)=−4x2+221x−650. Find the profit when 23 units are sold.Answer: □\square□ dollars. Question Help: Message instructor Submit Question

Problem 6326

Graph y=53x−9y=\frac{5}{3} x-9y=35​x−9

Problem 6327

Problem 6328

27) Find the function of g(x)g(x)g(x) by using function f(x)f(x)f(x). A) g(x)=−f(x−3)+2g(x)=-f(x-3)+2g(x)=−f(x−3)+2 B) g(x)=−f(x+3)+6g(x)=-f(x+3)+6g(x)=−f(x+3)+6 C) g(x)=−f(3−x)+2g(x)=-f(3-x)+2g(x)=−f(3−x)+2 D) g(x)=−f(x−3)+6g(x)=-f(x-3)+6g(x)=−f(x−3)+6

Problem 6329

Problem 6330

Evaluate the indicated function for f(x)=x2+2f(x)=x^{2}+2f(x)=x2+2 and g(x)=x−3g(x)=x-3g(x)=x−3 (f+g)(2)(f+g)(2)=\begin{array}{c} (f+g)(2) \\ (f+g)(2)= \end{array}(f+g)(2)(f+g)(2)=​ Submit Answer

Problem 6331

1. a. Express cos⁡(x)\cos (x)cos(x) in terms of cot⁡(x)\cot (x)cot(x) and csc⁡(x)\csc (x)csc(x). b. Express csc⁡(x)\csc (x)csc(x) in terms of cos⁡(x)\cos (x)cos(x) and tan⁡(x)\tan (x)tan(x).

Problem 6332

Problem 6333

Problem 6334

覑 W Write a quadratic function with zeros 6 and 7. "新] Write your answer using the variable x and in standard form with a leading coefficient of 1 . f(x)=f(x)=f(x)= □\square□ 2 3 4

Problem 6335

[效, Write a quadratic function with zeros 7 and -4. [i]. Write your answer using the variable x and in standard form with a leading coefficient of 1. g(x)=g(x)=g(x)= □\square□ 2 3 4

Problem 6336

A one-to-one function is given. Write an equation for the inverse function. s(x)=2x+3s−1(x)=\begin{array}{r} s(x)=\frac{2}{x+3} \\ s^{-1}(x)= \end{array}s(x)=x+32​s−1(x)=​ □\square□

Problem 6337

Problem 6338

Part 1 of 4 (a) Show that f(x)=3x+3f(x)=3 x+3f(x)=3x+3 defines a one-to-one function.A function is one-to-one if it can be shown that if f(a)=f(b)f(a)=f(b)f(a)=f(b), then □=□\square=\square□=□. Assume f(a)=f(b)f(a)=f(b)f(a)=f(b).

Problem 6339

(c) Estimate ∫04(x2+1)dx\int_{0}^{4}\left(x^{2}+1\right) d x∫04​(x2+1)dx using a right-hand sum with n=3n=3n=3 (i.e. R3)\left.R_{3}\right)R3​).Round your answer to two decimal places. R3=R_{3}=R3​= □\square□

Problem 6340

Part: 0/80 / 80/8Part 1 of 8 (a) Graph f(x)=x2−2;x≤0f(x)=x^{2}-2 ; x \leq 0f(x)=x2−2;x≤0.

Problem 6341

Question Evaluate the function f(x)=3log⁡(x+7)+2f(x)=3 \log (x+7)+2f(x)=3log(x+7)+2 for x=1x=1x=1. Round the final answer to the nearest two decimal places.

Problem 6342

Problem 6343

Part 1 of 9 (a) Graph f(x)=x+3f(x)=\sqrt{x+3}f(x)=x+3​.

Problem 6344

Problem 6345

Translate each graph as specified below. (a) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=(x−1)2y=(x-1)^{2}y=(x−1)2. (b) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=x2+2y=x^{2}+2y=x2+2.

Problem 6346

9 El diagrama muestra el gráfico de y=2x+3y=2^{x}+3y=2x+3. La curva pasa por los puntos A(0,a)\mathrm{A}(0, a)A(0,a) y B(1,b)\mathrm{B}(1, b)B(1,b). a Halle el valor de aaa y el valor de bbb. b Escriba la ecuación de la asíntota de la curva.

Problem 6347

Problem 6348

Problem 6349

y=(4+x)−1/2,a=0y=(4+x)^{-1 / 2}, \quad a=0y=(4+x)−1/2,a=0Find the Linearization at x=ax=ax=a. L(x)=L(x)=L(x)=

Problem 6350

Problem 6351

Write the domain in interval notation. f(x)=ln⁡(x2+9)f(x)=\ln \left(x^{2}+9\right)f(x)=ln(x2+9)The domain is □\square□

How much money must you invest now at $4.1 \%$ interest compounded continuously in order to have $\$ 10,000$ at the end of 4 years?
You must invest \\square$ (Round to the nearest cent as needed.)

Use the graph of the function to answer the question. (s) 2017 StrongMind. Created using GeoGebra.
What is the output of the function when the input is 0 ? Enter your answer as a number, like this: 42

Let $A(t)=4000 e^{0.06 t}$ be the balance in a savings account after $t$ years. Complete parts (a) through (f) below. (a) How much money was originally deposited?
There was $\$$ $\square$ originally deposited. (Type an integer or a decimal.)

1. Find the minimum value of $2 x^{2}+12 x+4$ and the value/values of $x$ where the minimum is attained.

$\int t e^{4 t} d t$

$\int \cos ^{4} \theta \sin ^{3} \theta d \theta$

$\int_{1}^{4} \frac{5 x+1}{\sqrt{x^{3}}} d x$

ما قيبة $\lim _{x \rightarrow-3} \frac{x^{3}+27}{x^{2}+4 x+3}=$
اخترأحد الذيارات $\frac{2}{27}$ $\frac{-27}{2}$ $\frac{27}{2}$ $\frac{-2}{27}$

إذا كانت $\lim _{x \rightarrow 1}\left(\frac{f(x)-f(1)}{x-1}\right)=10 \text { ركت } f(x)=m x^{2}$
فإن قيمة m تساوي اخترأحد الخيارات a. 2 b. 5 c. 3 d. 1

Let $f(x)=-3 x+4$ . Then $f^{-1}(x)=$

Given $f(x)=3 x+9$ a) Evaluate $f(5)$ $f(5)=$ $\square$ b) Evaluate $f(-4)$ $f(-4)=$ $\square$ Question Help: $\square$ Message instructor

Suppose that a company's profit (in terms of $x$ , the number of units sold) is given by the model $P(x)=-4 x^{2}+221 x-650$ . Find the profit when 23 units are sold.
Answer: $\square$ dollars. Question Help: Message instructor Submit Question

Graph $y=\frac{5}{3} x-9$

27) Find the function of $g(x)$ by using function $f(x)$ . A) $g(x)=-f(x-3)+2$ B) $g(x)=-f(x+3)+6$ C) $g(x)=-f(3-x)+2$ D) $g(x)=-f(x-3)+6$

Evaluate the indicated function for $f(x)=x^{2}+2$ and $g(x)=x-3$ $\begin{array}{c} (f+g)(2) \\ (f+g)(2)= \end{array}$ Submit Answer

1. a. Express $\cos (x)$ in terms of $\cot (x)$ and $\csc (x)$ . b. Express $\csc (x)$ in terms of $\cos (x)$ and $\tan (x)$ .

覑 W Write a quadratic function with zeros 6 and 7. "新] Write your answer using the variable x and in standard form with a leading coefficient of 1 . $f(x)=$ $\square$ 2 3 4

[效, Write a quadratic function with zeros 7 and -4. [i]. Write your answer using the variable x and in standard form with a leading coefficient of 1. $g(x)=$ $\square$ 2 3 4

A one-to-one function is given. Write an equation for the inverse function. $\begin{array}{r} s(x)=\frac{2}{x+3} \\ s^{-1}(x)= \end{array}$ $\square$

Part 1 of 4 (a) Show that $f(x)=3 x+3$ defines a one-to-one function.
A function is one-to-one if it can be shown that if $f(a)=f(b)$ , then $\square=\square$ . Assume $f(a)=f(b)$ .

(c) Estimate $\int_{0}^{4}\left(x^{2}+1\right) d x$ using a right-hand sum with $n=3$ (i.e. $\left.R_{3}\right)$ .
Round your answer to two decimal places. $R_{3}=$ $\square$

Part: $0 / 8$
Part 1 of 8 (a) Graph $f(x)=x^{2}-2 ; x \leq 0$ .

Question Evaluate the function $f(x)=3 \log (x+7)+2$ for $x=1$ . Round the final answer to the nearest two decimal places.

Part 1 of 9 (a) Graph $f(x)=\sqrt{x+3}$ .

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x-1)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}+2$ .

9 El diagrama muestra el gráfico de $y=2^{x}+3$ . La curva pasa por los puntos $\mathrm{A}(0, a)$ y $\mathrm{B}(1, b)$ . a Halle el valor de $a$ y el valor de $b$ . b Escriba la ecuación de la asíntota de la curva.

$y=(4+x)^{-1 / 2}, \quad a=0$
Find the Linearization at $x=a$ . $L(x)=$

Write the domain in interval notation. $f(x)=\ln \left(x^{2}+9\right)$
The domain is $\square$

Which point is on the graph of $f(x)=3 \cdot 5^{x} ?$ A. $(1,15)$ B. $(15,1)$ C. $(0,0)$ D. $(0,15)$

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If $f(x)=x^{5}+5 x^{4}+4$ , then what is the remainder when $f(x)$ is divided by $x+3$ ?
Answer Attempt 1 out of 2

```latex \begin{align} &\text{1-F: } [-1,8) \rightarrow \mathbb{R} \\ &F(x) = -2x - 5 \\ &\text{Fonk. İnceleyelim (Grafik, artanlık-azalanlık, max-min, Fonk. Sıfır., Fonksiyonun işareti)} \\ &F(x) = 2 \\ &f(x) \text{ örten} \end{align}

19 Die Verkaufszahlen (in 1000 Stück) einer neuen Schokolade werden durch die Funktion f mit $f(t)=4-4 \cdot e^{-0,1 t}$ beschrieben ( $t$ in Wochen). Berechnen Sie, wann die Verkaufszahlen innerhalb einer Woche um hundert Stück zunehmen.

The diagram shows part of the graph of $y=a+b \sin x$ . Find the values of the constants $a$ and $b$ . $\qquad$ $\qquad$

$g(x)=-2 \cos \left(\frac{1}{3}\left(x+20^{\circ}\right)\right)+4$ e. State the equation of the axis of the curve f. State the amplitude g. State the period h. Does this sinusoidal function have a plase stifs to the lef or righte?

(25علا
اوجد $\frac{d y}{d x}$ للالدجراثات اليالية: $y=\frac{\tan (2 x)}{x^{2}+1}$

\begin{align} 1) & \quad f(x) = 1 - 4x + x^5 \\ 2) & \quad f(x) = x^2 + 3 \\ 3) & \quad f(x) = 4 - x^2 \\ 4) & \quad f(x) = 2x^2 + 8x + 7 \\ 5) & \quad f(x) = -x^2 + 10x - 22 \\ 6) & \quad f(x) = 4x^2 + 24x \\ 7) & \quad f(x) = 6x - x^2 \\ \end{align}
Find the range of each function listed above.

8 Gegeben ist die Funktion $f$ mit $f(x)=e^{2 x}$ a) Skizzieren Sie den Graphen von f.