Browse Function problems Studdy Solved!

Problem 2101

What is the ratio for cosine Opp/Adj Opp/Hyp Hyp/Opp Adj/Hyp

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Problem 2102

When a pendulum 0.5 m long swings back and forth, its angular displacement $\theta$ from rest position, in radians, is given by $\theta(t)=\frac{1}{4} \sin \left(\frac{\pi}{2} t\right)$ , where $t$ is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (Assume the pendulum is at its rest position at $t=0$ .) $\checkmark \checkmark \checkmark \checkmark \checkmark$ $1 \mathrm{~cm}=\frac{1}{100} \mathrm{~m} \quad L=0.5 \mathrm{~m} \quad \sin (\theta)=\frac{\text { vertical displacement }}{\text { pendulum length }}$

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Problem 2103

Fill in the table using this function rule. $y=-10 x+2$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-1 & $\square$ \\ \hline 0 & $\square$ \\ \hline 1 & $\square$ \\ \hline 5 & $\square$ \\ \hline \end{tabular}

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Problem 2104

This table displays a scenario. \begin{tabular}{|c|c|} \hline Gallons, $\boldsymbol{g}$ & Liters, $\boldsymbol{l}$ \\ \hline 1 & 3.79 \\ \hline 2 & 7.58 \\ \hline 3 & 11.37 \\ \hline 4 & 15.16 \\ \hline 5 & 18.95 \\ \hline 6 & 22.74 \\ \hline \end{tabular}
What can be determined from the table? Check all that apply. The independent variable is the number of gallons. Liters is a function of Gallons. The equation $l=3.79 \mathrm{~g}$ represents the table. As the number of gallons increases, the number of liters increases. This is a function because every input has exactly one output.

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Problem 2105

Bestimme die lineare Funktionsgleichung, a) $m=2 ; P(-1 \mid-5)$

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Problem 2106

Consider the following functions. $f(x)=x^{2}-3 \text { and } g(x)=x-3$
Step 1 of 2: Find the formula for $(\mathrm{f} \cdot \mathrm{g})(\mathrm{x})$ and simplify your answer.

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Problem 2107

At a certain ocean bay, the maximum height of the water is 4 m above mean sea level at 8:00 a.m. The height is at a maximum again at 8:24 p.m. Assuming that the relationship between the height, $h$ , in metres, and the time, $t$ , in hours, is sinusoidal, determine the height of the water above mean sea level at 10:00 a.m.

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Problem 2108

9. Use an appropriate substitution to evaluate the definite integral $\int_{2}^{6} \frac{x}{\sqrt{2 x-3}} d x$ .

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Problem 2109

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -6 and 2 , and goes to $-\infty$ as $x \rightarrow-\infty$ .
Answer

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Problem 2110

have elapsed we use the first formula. If more than 3 hours and up to 5 hours have elapsed, we use the second formula.
Use the formula below to determine each of the following values. Pay attention to the value of to make sure you are using the correct formula! $d=\left\{\begin{array}{ccc} 2 t & \text { if } & 0 \leq t \leq 3 \\ 4(t-3)+6 & \text { if } & 3<t \leq 5 \end{array}\right.$ a. If $t=1.75$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches. b. If $t=4.25$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches. c. If $t=2.9$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches. d. If $t=3.1$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches.
Submit Question 5. Points possible: 4 License Unlimited attempts. Message instructor about this question menes per hour for 1.5 hours $(4.5-3=1.5)$ . At $5: 00 \mathrm{pm}$ , th has only been falling at a rate of 4 inches per hour for 2 hours $5-3=2$ ). cements s. /Learning 47 alytics se Syllabus $d=4(t-3)+6$
Putting everything together we have so far, we get the following. This notation indicates that $d$ us represented differently dependin on how much time has passed. $d=\left\{\begin{array}{ccc} 2 t & \text { if } & 0 \leq t \leq 3 \\ 4(t-3)+6 & \text { if } & 3<t \leq 5 \end{array}\right.$
If between 0 and 3 hours nave elapsed we use the first formula. If more than 3 hours and up to 5 hours have elapsed, we use the sec formula.
Use the formula below to determine each of the following values. Pay attention to the value of to make sure you are using the correct formula!

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Problem 2111

Between 2000 and 2020, the population of Mathville could be modeled by the function $m(t)=100 \sqrt[3]{t}$ , where $m(t)$ is the number of people in Mathville, and $t$ is the number of years since 2000. Between those same years, the population of Calcfield could be modeled by the function $c(t)=18 t$ . A. Graph each function on graph paper or a neatly made coordinate grid by hand. Be sure to consider an appropriate domain for the functions as you make your graph. B. Approximately where do the functions intersect? What does this point of intersection represent? C. Write and solve an equation to algebraically confirm where the two functions intersect. Show your work. D. Write 2-3 complete sentences comparing the relative populations of the cities over time.

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Problem 2112

2. When a pendulum 0.5 m long swings back and forth, its angular displacement $\theta$ from rest position, in radians, is given by $\theta(t)=\frac{1}{4} \sin \left(\frac{\pi}{2} t\right)$ , where $t$ is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (Assume the pendulum is at its rest position at $t=0$ .) $\checkmark \checkmark \checkmark \checkmark \checkmark$ $1 \mathrm{~cm}=\frac{1}{100} \mathrm{~m} \quad L=0.5 \mathrm{~m} \quad \sin (\theta)=\frac{\text { vertical displacement }}{\text { pendulumlength }}$

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Problem 2113

2. When a pendulum 0.5 m long swings back and forth, its angular displacement $\theta$ from rest position, in radians, is given by $\theta(t)=\frac{1}{4} \sin \left(\frac{\pi}{2} t\right)$ , where $t$ is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (Assume the pendulum is at its rest position at $t=0$ .) $\checkmark \checkmark \checkmark \checkmark \checkmark$ $\begin{aligned} 1 \mathrm{~cm} & =\frac{1}{100} \mathrm{~m} \end{aligned} \quad L=0.5 \mathrm{~m} \quad \sin (\theta)=\frac{\text { vertical displacement }}{\text { pendulum length }}$

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Problem 2114

2. When a pendulum 0.5 m long swings back and forth, its angular displacement $\theta$ from rest position, in radians, is given by $\theta(t)=\frac{1}{4} \sin \left(\frac{\pi}{2} t\right)$ , where $t$ is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (Assume the pendulum is at its rest position at $t=0$ .) $\checkmark \checkmark \checkmark \checkmark \checkmark$ $\begin{aligned} 1 \mathrm{~cm} & =\frac{1}{100} \mathrm{~m} \end{aligned} \quad L=0.5 \mathrm{~m} \quad \sin (\theta)=\frac{\text { vertical displacement }}{\text { pendulum length }}$

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Problem 2115

8 (VCAA-type question) The following data can be modelled by $y=k \log _{10}(x)+c$ . \begin{tabular}{|c|c|c|c|c|} \hline $x$ & 1 & 10 & 100 & 1000 \\ \hline $y$ & 5 & 105 & 205 & 305 \\ \hline \end{tabular}
The values of $k$ and $c$ respectively are: A 1 and 5 B 1 and 105 C 10 and 15 D 100 and 5 300 and 50

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Problem 2116

(VCAA-type question) The rule connecting $y$ and $x$ as shown in the graph is: A $y=2 x$ B $y=2 x^{2}$ c $y=2 \sqrt{x}$ D $y=\frac{1}{2} x$ E $y=x^{2}+2$

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Problem 2117

10. 设函数 $f(x)=(x-1)^{2}(x-4)$ . 则 A. $x=3$ 是 $f(x)$ 的极小值点 B. 当 $0<x<1$ 时, $f(x)<f\left(x^{2}\right)$ C. 当 $1<x<2$ 时, $-4<f(2 x-1)<0$ D. 当 $-1<x<0$ 时, $f(2-x)>f(x)$

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Problem 2118

2. Consider the function $g(x)=-2 \log _{2}\left[\frac{1}{2}(x+4)\right]+6$ a) State the transformations (in the correct order) that are applied to $f(x)=\log _{2} x$ to obtain the graph of $y=g(x)$ . [2] b) State the mapping formula required for this transformation. [1] $(x, y) \rightarrow$ $\qquad$ [6 Marks] c) Sketch: Show and label 4 key points as well as any asymptote (include the equation). [3]

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Problem 2119

The graph of $y=x^{2}$ is the solid black graph below. Which function represents the dotted graph?

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Problem 2120

Question 4 of 25
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. $\{2,4,6,8\}$ B. $\{3,4,5,6\}$ C. $(2,3),(4,4),(6,5),(8,6)$ D. $\{2,3,4,5,6,8\}$ SUBMIT

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Problem 2121

Consider the function $g(x)=-2 \log _{2}\left[\frac{1}{2}(x+4)\right]+6$ [6 Marks] state the transformations (in the correct order) that are applied $(x)=\log _{2} x$ to obtain the graph of $y=g(x)$ . Horizontal shift to the left by 4 units. horizontal compression by a factor of 2 . vertical stretch by afactor of and a reflection over $x$ -axis- vertical shift 6 units up. tate the mapping formula required for this sformation. [1] $(x, y) \rightarrow\left(\frac{x}{2}-4,-2 y+6\right)$ c) Sketch: Show and label 4 key points as well as any asymptote (include the equation). [3]

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Problem 2122

The figure below shows the graph of a rational function $f$ . Keyboard
It has vertical asymptotes $x=-2$ and $x=3$ , and horizontal asymptote $y=0$ . The graph does not have an $x$ -intercept, and it passes through the point $(1,-1)$ . The equation for $f(x)$ has one of the five forms shown below. Choose the appropriate form for $f(x)$ , and then write the equation. You can assume that $f(x)$ is in simplest form. $f(x)=\frac{a}{x-b}$ $\square$ $\square$ $f(x)=\frac{a(x-b)}{x-c}$ $=\frac{\square(\square}{\square}$ $f(x)=\frac{a}{(x-b)(x-c)}=\frac{\square}{\square)(\square)}$ $\square$ $f(x)=\frac{a(x-b)}{(x-c)(x-d)}=\frac{\square(\square)}{\square(\square)}$ $\square$

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Problem 2123

6) An observer stands 700 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of $900 \mathrm{ft} / \mathrm{sec}$ . Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 2400 ft from the ground?

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Problem 2124

Blood pressure can be modeled by a sinusoidal curve, where the maximum and minimum on the curve correlate to the person's blood pressure reading. Henry's blood pressure is modeled by the function $P(t)=30 \sin (2 \pi t)+100$ , where $t$ is time in seconds.
Which graph accurately depicts this model?

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Problem 2125

Tides in a specific location can be approximated using the periodic function shown on the graph.
What is the interpretation of the amplitude in this application?

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Problem 2126

Consider the function $y=2^{-x}+3$ a) Find the $y$ -value of the $y$ -intercept of the curve $y=2^{-x}+3$ . $y=4$ ...
Find the equation of the horizontal asymptote of the curve $y=2^{-x}+3$ Enter your next step here

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Problem 2127

$\begin{array}{l}f(x)=10 \sqrt{95+x} \\ f(49)=\square\end{array}$

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Problem 2128

$\begin{array}{l}f(x)=(4-x)^{2} \\ f(11)=\square\end{array}$

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Problem 2129

(1 point) Let $f(x)=(\ln (x))^{\operatorname{sed}(x)}$ . Find $f^{\prime}(x)$ . $f^{\prime}(x)=$

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Problem 2130

$\begin{array}{l}f(x)=7 \sqrt{x-155} \\ f(159)=\end{array}$

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Problem 2131

$\begin{array}{l}f(x)=(1+x)^{2} \\ f(9)=\square\end{array}$

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Problem 2132

$\begin{array}{l}f(r)=r^{2} \\ f(d-6)=\end{array}$

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Problem 2133

$\begin{array}{l}f(y)=y^{2}-10 y \\ f(s+2)=\end{array}$

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Problem 2134

2) $\sin X$

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Problem 2135

Crowdmark linear approximation of sc test-3-07073 $-x^{1}-1$ $-\cot (x)-0.5$ $\ln |x|-0.5$
Q2 X18 (20 pts) Sketch the graph of a function $f(x)$ satisfying the following: $\lim _{x \rightarrow \infty} f(x)=3 \quad \lim _{x \rightarrow-\infty} f(x)=2$
Increasing on $(-\infty,-4) \cup(1, \infty)$
Concave up on $(-\infty, 1)$ Concave down on $(1, \infty)$ minimum at $(1,0)$
Vertical Asymptote at $x=-4$ Dccrcasing on $(-4,1)$
1 Concavity -2

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Problem 2136

NASA launches a rocket at $t=0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t)=-4.9 t^{2}+295 t+339$ .
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after $\square$ seconds.
How high above sea-level does the rocket get at its peak?
The rocket peaks at $\square$ meters above sea-level.

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Problem 2137

نعثر الدالة $f$ المعر فلة على

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Problem 2138

You have a wire that is 38 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when $A$ is a minimum?
The circumference of the circle is $\square$ cm.
Give your answer to two decimal places

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Problem 2139

You have a wire that is 53 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when $A$ is a minimum?
The circumference of the circle is 23.30 $\square$ cm .
Give your answer to two decimal places

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Problem 2140

1. If $f(x)=2 x^{2}+4$ , which of the following will calculate the derivative of $f(x)$ ? (a) $\frac{\left[2(x+\Delta x)^{2}+4\right]-\left(2 x^{2}+4\right)}{\Delta x}$ (b) $\lim _{\Delta x \rightarrow 0} \frac{\left(2 x^{2}+4+\Delta x\right)-\left(2 x^{2}+4\right)}{\Delta x}$ (c) $\lim _{\Delta x \rightarrow 0} \frac{\left[2(x+\Delta x)^{2}+4\right]-\left(2 x^{2}+4\right)}{\Delta x}$ (d) $\frac{\left(2 x^{2}+4+\Delta x\right)-\left(2 x^{2}+4\right)}{\Delta x}$ (e) None of these

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Problem 2141

For problems 11-14, use proper notation throughout. 11.) Consider the function $f(t)$ Int a.) Calculate the instantancous rate of change of the function at $t=\frac{1}{2}$ , b.) Find the equation of the tangent line at the point where $t=3$ . Leave your answer in terms of the natural logarithm.

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Problem 2142

Review: Assessment 11 (practice questions) Score: 0/13 Answered: 0/13
Question 1
Recall that functions can be described in words, graphs, tables, and equations. Which of the following functions are periodic functions? [Tip: Use a calculator to graph the function(s), if helpful.] $y=2 \sin (-0.5 x)+1$ $y=\sec (1 x)+2$ $y=2 x+1$ $y=-0.5 \cos (x)+3$ $y=1 x^{2}+2 x+3$

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Problem 2143

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=48 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

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Problem 2144

12.) Find the following using the Limit Definition of Derivative. You should be able to do this with very little computation. \begin{tabular}{|l|l|} \hline a.) $\lim _{\Delta x \rightarrow 0} \frac{\sin (x+\Delta x)-\sin (x)}{\Delta x}$ & b.) $\lim _{h \rightarrow 0} \frac{(x+h)^{2}-x^{2}}{h}$ \\ c.) $\lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x-\sin \frac{\pi}{4}}{x-\frac{\pi}{4}}$ & d.) $\lim _{h \rightarrow 0} \frac{\sin \left(\frac{\pi}{6}+h\right)-\frac{1}{2}}{h}$ \\ \hline e.) $\lim _{\Delta x \rightarrow 0} \frac{(2+\Delta x)^{3}-8}{\Delta x}$ & f.) $\lim _{x \rightarrow \pi} \frac{\cos x+1}{x-\pi}$ \\ \hline & \\ \hline \end{tabular}

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Problem 2145

5. Find $\frac{d^{2} y}{d x^{2}}$ for $y=\frac{x+3}{x-1}$ (a) 0 (b) $\frac{-8}{(x-1)^{3}}$ (c) $\frac{-4}{(x-1)^{3}}$ (d) $\frac{8}{(x-1)^{3}}$ (e) None of these

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Problem 2146

3. Find the a bsolute max and min $f(x)=x^{\frac{3}{2}}-3 \sqrt{x}, 0 \leq x \leq 4$ $\begin{array}{l} f(x)=x^{\frac{3}{2}}-\frac{3 x^{\frac{1}{2}}}{} \\ f^{\prime}(x)=\frac{3}{2} x^{\frac{1}{2}}-\frac{3}{2} x^{-\frac{1}{2}} \end{array}$

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Problem 2147

A storage company rents out moving trucks for an initial rental fee plus an amount based on the number of miles driven. The values in the table represent the linear relationship between the number of miles driven and the total amount of the rental in dollars.
Truck Rental \begin{tabular}{|c|c|} \hline Number of Miles Driven & Total Cost \\ \hline 0 & $\$ 25.00$ \\ \hline 30 & $\$ 47.50$ \\ \hline 45 & $\$ 58.75$ \\ \hline 50 & $\$ 62.50$ \\ \hline 60 & $\$ 70.00$ \\ \hline 75 & $\$ 81.25$ \\ \hline \end{tabular}
What is the rate of change of the total cost in dollars with respect to the number of miles driven? Enter your answer in the box. \$ per mile driven Submit Answer Show Hint

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Problem 2148

8. Find $y^{\prime}$ if $y=\sin (x+y)$ . (a) 0 (b) $\frac{\cos (x+y)}{1-\cos (x+y)}$ (c) $\cos (x+y)$ (d) 1 (c) None of these

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Problem 2149

12.) Find the following using the Limit Definition of Derivative. You should be able to do this with very little computation. g.) $\lim _{x \rightarrow 2} \frac{\ln x-\ln 2}{x-2}$ h.) $\lim _{\Delta x \rightarrow 0} \frac{(3+\Delta x)^{2}+(3+\Delta x)-12}{\Delta x}$

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Problem 2150

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=112 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

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Problem 2151

प्रा II thatam 11 Badt to intro Paga Mark $=$ Complete saved in both accounts over fine. A. What does $(0)$ represent in the context of this problem? (1 point) B B 1 It represents the inkst amaurt of money Jase had in her savinge account 13 / 100 Whord Limit B. Build a function to represent the total amouni of monay Jada has saved over time in both accounts cumbined. (2 poltis)
B $\square$ C. How much mongy does Jeda make per hour? Wilk your answer as a whole number, (1 point)
5 $\square$ per hour Search

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Problem 2152

C. $\sin \frac{\pi}{8}$

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Problem 2153

```latex A manufacturer of tennis rackets finds that the total cost $C(x)$ (in dollars) of manufacturing $x$ rackets/day is given by $C(x)=400+4x+0.0001x^{2}$ . Each racket can be sold at a price of $p$ dollars, where $p$ is related to $x$ by the demand equation $p=10-0.0004x$ . If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer. ```

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Problem 2154

Submit Answer
8. [-/1 Points]
DETAILS MY NOTES The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure.
Let $x=$ the distance from the left end of the pool. Determine $\Delta x$ if the midpoint rule with $n=4$ will be used to estimate the area (in $\mathrm{m}^{2}$ ) of the pool. $\Delta x=$ $\square$ Use the midpoint rule with $n=4$ to estimate the area (in $\mathrm{m}^{2}$ ) of the pool. $\square$ $m^{2}$ Submit Answer Home My Assignments Request Exten

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Problem 2155

Travail sur la fonction rationnelle $z$
Rappel : Si tu n'es pas sûr đ'une réponse, tu as le droit de me poser une question.... Tu fais ton travail sur une feuille PROPRE et tu COMMUNIQUES ta démarche. Le but premier de ce travail est de te rendre apte à travailler la fonction rationnelle. Je t'encourage à valider tes réponses avec Desmos, mais les démarches algébriques sont obligatoires. Numéro 1. A) Fais Y'́tude complète de la fonction rationnelle suivante $f(x)=\frac{54 x-513}{6 x-60}$ L'étude complète veut dire : 1) Déterminer la règle sous la forme $f(x)=\frac{a}{x-h}+k$ $f(x)=\frac{\frac{9}{2}}{x-10}+9$ 2) Représentation graphique, avec les asymptotes $\rightarrow \rightarrow \rightarrow$ 3) Domaine $\qquad$ Codomaine $\qquad$ P) \{a\} 4) Abscisse à Porigine et ordonnée à l'origine (AVEC CALCULS) $y=8,55$ 5) La variation $\qquad$ Décroissante $\rightarrow \mathbb{R} \backslash\{10\}$ 6) Le signe $\qquad$ 10. 400 $\qquad$ Negative $[a, 5,10[$ 7) Les extrémums (s'il y en a) $\qquad$ B) Détermine lintervalle pour lequel $f(x) \leq 17$ . AVEC CALCULS... $\text { RÉPONSE: } \frac{x \in]-\infty, 10\left[\cup \left[\frac{169}{16}\right.\right.}{16}+\infty[$ $2^{\circ}$ numéro à faire au verso...

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Problem 2156

49. Maximizing Profit A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $\$ 20,000$ , and the variable cost for producing $x$ pagers per week is $V(x)=0.000001 x^{3}-0.01 x^{2}+50 x$ dollars. The company realizes a revenue of $R(x)=-0.02 x^{2}+150 x \quad(0 \leq x \leq 7500)$ dollars from the sale of $x$ pagers/week. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula.

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Problem 2157

Between 2000 and 2020, the population of Mathville could be modeled by the function $m(t)=100 \sqrt[3]{t}$ , where $m(t)$ is the number of people in Mathville, and $t$ is the number of years since 2000. Between those same years, the population of Calcfield could be modeled by the function $c(t)=18 t$ . A. Graph each function on graph paper or a neatly made coordinate grid by hand. Be sure to consider an appropriate domain for the functions as you make your graph. B. Approximately where do the functions intersect? What does this point of intersection represent? C. Write and solve an equation to algebraically confirm where the two functions intersect. Show your work. D. Write 2-3 complete sentences comparing the relative populations of the cities over time (10 points)

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Problem 2158

Problem 5. Use the change-of-base theorem to write each logarithm (i) in terms of common logarithms, (ii) in terms of natural logarithms. Approximation the answer to four decimal places for each logarithm. (a) $\log _{4} 20$ (b) $\log _{2} 0.7$

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Problem 2159

Compute the derivatives of the given functions. a) $f(r)=10^{r} . \quad f^{\prime}(r)=$ $\square$ . b) $g(s)=17^{9} . \quad g^{\prime}(s)=$ $\square$ . b) $h(t)=\frac{5^{t}}{6^{t}} \quad h^{\prime}(t)=$ $\square$ .

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Problem 2160

Which is the graph of $y=\cos (x)+3$ ?

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Problem 2161

1 The functions $f$ and $g$ are defined by $f(x)=2 \ln (x+3), x>-3$ and $g(x)=\mathrm{e}^{k x}-3, x \in \mathbb{R}$ , where $k$ is a constant. The function g is the inverse of function f . (a) Determine the value of $k$ . [4 marks] (b) Sketch the graphs of $f$ and $g$ on the same axes. [5 marks]

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Problem 2162

10. [0/1 Points] DETAILS
MYNOTES
Find the absolute maximum and absolute minimum values of $f$ on the given interval. $f(x)=4 x^{3}-6 x^{2}-144 x+1, \quad[-4,5]$ absolute minimum $\square$ $\square$ absolute maximum Need Help? Readit $\square$ Watchlt $\square$ $\square$ Masterlit

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Problem 2163

points) $f(x)=\sin (\sin (x))$ then $f^{\prime}(x)=\square$ Preview My Answers Submit Answers

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Problem 2164

$\begin{array}{l} \frac{y=2x^{3}-7x^{2}-7x+12}{2(-1)^{3}-7(-1)^{2}-7(-1)+12+1+12} \\ = \frac{1-12}{+2+6} \\ -2+6 \\ +3+4 \\ -3-4 \end{array}$

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Problem 2165

Which of the following functions has a graph that is symmetric about the $y$ -axis?
Select all that apply. A. $y=\frac{1}{x}$ B. $y=\sqrt{x}$ C. $y=|x|$ D. $y=x^{3}$

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Problem 2166

(1 point) Please answer the following questions about the function $f(x)=\frac{2 x^{2}}{x^{2}-25}$
Instructions: - If you are asked for a function, enter a function. - If you are asked to find $x$ - or $y$ -values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. - If you are asked to find an interval or union of intervals, use interval notation. Enter \{ \} if an interval is empty. - If you are asked to find a limit, enter either a number, I for $\infty,-I$ for $-\infty$ , or $D N E$ if the limit does not exist. (a) Calculate the first derivative of $f$ . Find the critical numbers of $f$ , where it is increasing and decreasing, and its local extrema. $f^{\prime}(x)=$ $\square$ Critical numbers $x=$ $\square$ Union of the intervals where $f(x)$ is increasing $\square$ Union of the intervals where $f(x)$ is decreasing $\square$ Local maxima $x=$ $\square$ Local minima $x=$ $\square$ (b) Find the following left- and right-hand limits at the vertical asymptote $x=-5$ . $\lim _{x \rightarrow-5^{-}} \frac{2 x^{2}}{x^{2}-25}=$ $\square$ $\lim _{x \rightarrow-5^{+}} \frac{2 x^{2}}{x^{2}-25}=?$ $\square$ Find the following left-and right-hand limits at the vertical asymptote $x=5$ . $\lim _{x \rightarrow 5^{-}} \frac{2 x^{2}}{x^{2}-25}=?$ $\square$ $\lim _{x \rightarrow 5^{+}} \frac{2 x^{2}}{x^{2}-25}=$ $\square$ Find the following limits at infinity to determine any horizontal asymptotes. $\lim _{x \rightarrow-\infty} \frac{2 x^{2}}{x^{2}-25}=? \quad \vee \quad \lim _{x \rightarrow+\infty} \frac{2 x^{2}}{x^{2}-25}=?$ $\square$ $\square$ (c) Calculate the second derivative of $f$ . Find where $f$ is concave up, concave down, and has inflection points. $f^{\prime \prime}(x)=\square$
Union of the intervals where $f(x)$ is concave up $\square$ Union of the intervals where $f(x)$ is concave down $\square$ $\square$ Inflection points $x=$

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Problem 2167

2. find the zeres and verten for the function $f(x)=3 x^{2}+12 x-135$

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Problem 2168

I'm sorry, but I can't assist with that request.

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Problem 2169

Suppose that $f(x)=(5-\ln (x))^{3}$ . Find $f^{\prime}(1)$ . $f^{\prime}(1)=$

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Problem 2170

7) A rectangular enclosure is bounded on one side by a river and on the other 3 sides by a total of 100 m of fencing. Find the dimensions of the largest possible enclosure.

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Problem 2171

Use synthetic division and the remainder theorem to find $P(a)$ . $\begin{array}{l} P(x)=x^{3}+6 x^{2}-7 x+6 ; a=3 \\ P(a)=\square \end{array}$ $\square$ (Simplify your answer.)

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Problem 2172

Suppose that $f(x)=\frac{3}{\ln \left(x^{2}+2\right)}$
Find $f^{\prime}(1)$ . $f^{\prime}(1)=$

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Problem 2173

If $f(x)=(5 x+4)^{-1}$
Find $f^{\prime}(x)$ . Then $f^{\prime}(x)=$ $\square$ Find $f^{\prime}(3)$ . Then $f^{\prime}(3)=$ $\square$

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Problem 2174

(1 point) Let $f(x)=e^{-7 x^{2}}$ . Then $f(x)$ has a relative minimum at $x=$ a relative maximum at $x=\square$ and inflection points at $x=\square$ and at $x=\square$
Write DNE if any of the above do not exist. Write the inflection points (if ar

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Problem 2175

Determine, without graphing, whether the given quadratic function has a maximum value or a mir $f(x)=-4 x^{2}-16 x-9$
The quadratic function has a $\square$ value. minimum maximum

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Problem 2176

Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. (If an answer is undefined, enter UNDEFINED.) $y=\frac{25}{(x+5)^{2}},(0,1)$ $\square$ Need Help? Read It Submit Answer

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Problem 2177

Draw a line through the point $(-1,2)$ that is parallel to the graph of the line. Line
Undo Redo $\times$ Reset

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Problem 2178

Write the function whose graph is the graph of $y=\sqrt{x}$ but is shifted down 3 units. $\mathrm{y}=\square$

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Problem 2179

9. Given the polynomial $P(x)=-x(x+2)(x-4)^{2}(x-1)^{5}$ : a) Determine the multiplicity of each zero and describe the shape of the graph at each zero. \begin{tabular}{|l|l|l|} \hline $X$ - intercept & Multiplicity & Description of shape \\ \hline & & \\ \hline & & \\ \hline & & \\ \hline & & \\ \hline \end{tabular} b) State the degree of the polynomial. 1a 30-1 Outcomes 11 RF12

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Problem 2180

odule 5 Final culz Question 4 of 12 list
For the quadratic function $f(x)=x^{2}+6 x$ , answer parts (a) through ( $f$ ). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $\square$ (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $\square$ (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is $\square$ . (Type an integer or a simplified fraction.) B. There is no y-intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$ -intercept(s) is/are $\square$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$ -intercepts. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function. Click to enlarge graph (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $\square$ (Type your answer in interval notation.) The range of $f$ is $\square$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $\square$ . (Type your answer in interval notation.) The function is decresasing on the interval $\square$ . (Type your answer if interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct choice below and fill in the answer box(es) within your choice.

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Problem 2181

3. Determine la derivada direccional de $f(x, y)=2 x^{2} y^{3}+6 x y$ en $(1,1)$ en la dirección del vector unitario cuyo ángulo con el eje x positivo es $\frac{\pi}{6}$ . Además, determine el gradiente de fen ( 1,1 ) Recuerde: $u=\cos \theta i+\operatorname{sen} \theta j$

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Problem 2182

Use the Change of Base Formula to rewrite the logarithm with the common logarithm or the natural logarithm: $\begin{array}{l} \log _{3}(23) \\ \log _{3}(23)=\square \end{array}$
Use a calculator to evaluate the logarithm. Round to four decimal places. $\square$

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Problem 2183

Answer the questions about the following function. $f(x)=\frac{x+11}{x-12}$ (a) Is the point $\left(3,-\frac{17}{6}\right)$ on the graph of $f$ ? (b) If $\mathrm{x}=1$ , what is $\mathrm{f}(\mathrm{x})$ ? What point is on the graph of f ? (c) If $f(x)=2$ , what is $x$ ? What point(s) is/are on the graph of $f$ ? (d) What is the domain of $f$ ? (e) List the $x$ -intercepts, if any, of the graph of f . (f) List the $y$ -intercept, if there is one, of the graph of $f$ .

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Problem 2184

Find the average value of the function $f$ over the interval $[0,4]$ . $f(x)=\frac{12}{x+1}$ $\square$

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Problem 2185

$f(x)=\frac{x+10}{x-8}$ (a) Is the point $(3,-8)$ on the graph of $f$ ? (b) If $x=2$ , what is $f(x)$ ? What point is on the graph of $f$ ? (c) If $f(x)=2$ , what is $x$ ? What point(s) is/are on the graph of $f$ ? (d) What is the domain of $f$ ? (e) List the $x$ -intercepts, if any, of the graph of $f$ . (f) List the $y$ -intercept, if there is one, of the graph of $f$ .

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Problem 2186

Graphs of Rational Functions Nomo: Maluge

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Problem 2187

Question Given the function $f(x)=\frac{x}{1-4 x^{3}}$ , find $f^{\prime}(x)$ in simplified form.
Answer Attempt 1 out of 3

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Problem 2188

Question Given the function $y=\frac{3 x^{2}-2}{1-x^{2}}$ , find $\frac{d y}{d x}$ in simplified form.
Answer Attempt 1 out of 3

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Problem 2189

Find a polynomial of degree $n$ that has the given zero(s). (There are many correct answe $\begin{array}{r} x=0,-\sqrt{7}, \sqrt{7} ; n=5 \\ f(x)=x^{3}\left(x^{2}-6\right), x^{5}-7 x^{3} \end{array}$ Need Help? Read It

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Problem 2190

Question Watch Video Show Examples
Given the function $f(x)=x^{2}-5 x+0$ , determine the average rate of change of the function over the interval $-3 \leq x \leq 9$ .
Answer Attempt 1 out of 4 $\square$ Submit Answer

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Problem 2191

Use an appropriate Half-Angle Formula to find the exact value of the expression. $\sin \left(\frac{9 \pi}{8}\right)$

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Problem 2192

Let $\mathrm{g}(\mathrm{x})=9 \mathrm{x}^{2}-1$ (a) Find the average rate of change from -2 to 8. (b) Find an equation of the secant line containing ( $-2, g(-2)$ ) and ( $8, g(8)$ ). (a) The average rate of change from -2 to 8 is $\square$ . (Simplify your answer.) (b) An equation of the secant line containing ( $-2, g(-2))$ and $(8, g(8))$ is $\square$ . (Type your answer in slope-intercept form.)

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Problem 2193

(1 point) Suppose that $f(x)=x-7 x^{1 n}$ (A) Find all critical values of $f$ , If there are no critical values, onter -1000 . If there are more than one, enter them separated by commas.
Critical value $(\mathrm{s})=0,1$ (B) Use interval notation to indicate where $f(x)$ is increasing.
Note: When using interval notation in WeBWork, you use I for $\infty,-1$ for $-\infty$ , and $\mathbf{U}$ for the union symbol, If there are no values that satisfy the required condition, then enter " $00^{\circ}$ without the quotation marks. Increasing: $(-\infty, 0) \cup(1, \infty)$ (C) Use interval notation to indicate where $f(x)$ is decreasing.
Decreasing: $(0,1)$ (D) Find the $x$ -coordinates of all local maxima of $f$ . If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas.
Local maxima at $x=$ $\square$ (E) Find the $x$ -coordinates of all local minima of $f$ . If there are no local minima, enter -1000 . If there are more than one, enter them separated by commas.
Local minima at $x=1$ (A) Use interval notation to indicate where $f(x)$ is concave up.
Concave up: $(0, \infty)$ (G) Use interval notation to indicate where $f(x)$ is concave down.
Concave down: $(-\infty, 0)$ (H) Find all inflection points of $f$ . If there are no inflection points, enter -1000 . If there are more than one, enter them separated by commas.
Inflection point(s) at $x=$ $\square$ (1) Use all of the preceding information to sketch a graph of $f$ . When you're finished, enter a " 1 " in the box below.
Graph Complete: $\square$

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Problem 2194

$f(x)=x-7 x^{1 / 7}$ (A) Find all critical values of $f$ . If there are no critical values, enter -1000 . If there are more than one, enter them separated by commas.
Critical value $(s)=0,1$ . (B) Use interval notation to indicate where $f(x)$ is increasing.
Note: When using interval notation in WeBWorK, you use I for $\infty,-\mathrm{I}$ for $-\infty$ , and $\mathbf{U}$ for the union symbol. If there are no values that satisfy the required condition, then enter the quotation marks.
Increasing: $(-\infty, 0) \cup(1, \infty)$ (C) Use interval notation to indicate where $f(x)$ is decreasing.
Decreasing: $(0,1)$ (D) Find the $x$ -coordinates of all local maxima of $f$ . If there are no local maxima, enter -1000 . If there are more than one, enter them separated by commas.
Local maxima at $x=$ $\square$ 0 (E) Find the $x$ -coordinates of all local minima of $f$ . If there are no local minima, enter -1000 . If there are more than one, enter them separated by commas.
Local minima at $x=$ $\square$ (F) Use interval notation to indicate where $f(x)$ is concave up.
Concave up: $(0, \infty)$ (G) Use interval notation to indicate where $f(x)$ is concave down.
Concave down: $(-\infty, 0)$ (H) Find all inflection points of $f$ . If there are no inflection points, enter -1000 . If there are more than one, enter them separated by commas. Inflection point(s) at $x=$ $\square$

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Problem 2195

Find the domain, the x-intercept, and the y-intercept of the function $f(x) = \frac{5-2x}{x+4}$ .

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Problem 2196

find + simplify $f(x)=x^{2}-6$

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Problem 2197

find and simplify $f(x)=3 x^{2}-2 x$

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Problem 2198

corresponding side length of quadina
2 A triangle will be dilated on the coordinate grid to create a larger triangle. The triangle is dilated using the origin as the center of dilation. Write a rule that could represent this dilation. Write the correct answer in each box. Not all answers will be used. $0.25 x$ $\square$ $4 x$ $\square$ $x-1.5$ $\square$ $\square$ $y+1.5$
The triangle was dilated according to the rule $(x, y) \rightarrow($ $\square$ $\square$ ) e2024 登

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Problem 2199

For all problems, a polygon graphed on a coordinate grid will be dilated with the origin as the center of dilation.
1 If $(x, y)$ represents any point on the polygon, find the rule that represents the dilation that has been applied to the polygon if the scale factor is $\frac{2}{5}$ . $(x, y) \rightarrow($ $\qquad$ $\qquad$

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Problem 2200

Find the follow
2. $\lim _{x \rightarrow 0} \frac{x^{2}}{1-\cos (3 x)}$

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Function

Problem 2101

What is the ratio for cosine Opp/Adj Opp/Hyp Hyp/Opp Adj/Hyp

Problem 2102

Problem 2103

Fill in the table using this function rule. y=−10x+2y=-10 x+2y=−10x+2 \begin{tabular}{|c|c|} \hlinexxx & yyy \\ \hline-1 & □\square□ \\ \hline 0 & □\square□ \\ \hline 1 & □\square□ \\ \hline 5 & □\square□ \\ \hline \end{tabular}

Problem 2104

Problem 2105

Bestimme die lineare Funktionsgleichung, a) m=2;P(−1∣−5)m=2 ; P(-1 \mid-5)m=2;P(−1∣−5)

Problem 2106

Consider the following functions. f(x)=x2−3 and g(x)=x−3f(x)=x^{2}-3 \text { and } g(x)=x-3f(x)=x2−3 and g(x)=x−3Step 1 of 2: Find the formula for (f⋅g)(x)(\mathrm{f} \cdot \mathrm{g})(\mathrm{x})(f⋅g)(x) and simplify your answer.

Problem 2107

Problem 2108

9. Use an appropriate substitution to evaluate the definite integral ∫26x2x−3dx\int_{2}^{6} \frac{x}{\sqrt{2 x-3}} d x∫26​2x−3​x​dx.

Problem 2109

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -6 and 2 , and goes to −∞-\infty−∞ as x→−∞x \rightarrow-\inftyx→−∞.Answer

Problem 2110

Problem 2111

Problem 2112

Problem 2113

Problem 2114

Problem 2115

Problem 2116

(VCAA-type question) The rule connecting yyy and xxx as shown in the graph is: A y=2xy=2 xy=2x B y=2x2y=2 x^{2}y=2x2 c y=2xy=2 \sqrt{x}y=2x​ D y=12xy=\frac{1}{2} xy=21​x E y=x2+2y=x^{2}+2y=x2+2

Problem 2117

Problem 2118

Problem 2119

The graph of y=x2y=x^{2}y=x2 is the solid black graph below. Which function represents the dotted graph?

Problem 2120

Problem 2121

Problem 2122

Problem 2123

Problem 2124

Problem 2125

Tides in a specific location can be approximated using the periodic function shown on the graph.What is the interpretation of the amplitude in this application?

Problem 2126

Consider the function y=2−x+3y=2^{-x}+3y=2−x+3 a) Find the yyy-value of the yyy-intercept of the curve y=2−x+3y=2^{-x}+3y=2−x+3. y=4y=4y=4 ...Find the equation of the horizontal asymptote of the curve y=2−x+3y=2^{-x}+3y=2−x+3 Enter your next step here

Problem 2127

f(x)=1095+xf(49)=□\begin{array}{l}f(x)=10 \sqrt{95+x} \\ f(49)=\square\end{array}f(x)=1095+x​f(49)=□​

Problem 2128

f(x)=(4−x)2f(11)=□\begin{array}{l}f(x)=(4-x)^{2} \\ f(11)=\square\end{array}f(x)=(4−x)2f(11)=□​

Problem 2129

(1 point) Let f(x)=(ln⁡(x))sed⁡(x)f(x)=(\ln (x))^{\operatorname{sed}(x)}f(x)=(ln(x))sed(x). Find f′(x)f^{\prime}(x)f′(x). f′(x)=f^{\prime}(x)=f′(x)=

Problem 2130

f(x)=7x−155f(159)=\begin{array}{l}f(x)=7 \sqrt{x-155} \\ f(159)=\end{array}f(x)=7x−155​f(159)=​

Problem 2131

f(x)=(1+x)2f(9)=□\begin{array}{l}f(x)=(1+x)^{2} \\ f(9)=\square\end{array}f(x)=(1+x)2f(9)=□​

Problem 2132

f(r)=r2f(d−6)=\begin{array}{l}f(r)=r^{2} \\ f(d-6)=\end{array}f(r)=r2f(d−6)=​

Problem 2133

f(y)=y2−10yf(s+2)=\begin{array}{l}f(y)=y^{2}-10 y \\ f(s+2)=\end{array}f(y)=y2−10yf(s+2)=​

Problem 2134

2) sin⁡X\sin XsinX

Problem 2135

Problem 2136

Problem 2137

نعثر الدالة fff المعر فلة على

Problem 2138

Problem 2139

Problem 2140

Problem 2141

Problem 2142

Problem 2143

A ball is thrown vertically upward. After ttt seconds, its height hhh (in feet) is given by the function h(t)=48t−16t2h(t)=48 t-16 t^{2}h(t)=48t−16t2. After how long will it reach its maximum height?Do not round your answer.Time: □\square□ seconds

Problem 2144

Problem 2145

5. Find d2ydx2\frac{d^{2} y}{d x^{2}}dx2d2y​ for y=x+3x−1y=\frac{x+3}{x-1}y=x−1x+3​ (a) 0 (b) −8(x−1)3\frac{-8}{(x-1)^{3}}(x−1)3−8​ (c) −4(x−1)3\frac{-4}{(x-1)^{3}}(x−1)3−4​ (d) 8(x−1)3\frac{8}{(x-1)^{3}}(x−1)38​ (e) None of these

Problem 2146

Problem 2147

Problem 2148

8. Find y′y^{\prime}y′ if y=sin⁡(x+y)y=\sin (x+y)y=sin(x+y). (a) 0 (b) cos⁡(x+y)1−cos⁡(x+y)\frac{\cos (x+y)}{1-\cos (x+y)}1−cos(x+y)cos(x+y)​ (c) cos⁡(x+y)\cos (x+y)cos(x+y) (d) 1 (c) None of these

Problem 2149

Problem 2150

A ball is thrown vertically upward. After ttt seconds, its height hhh (in feet) is given by the function h(t)=112t−16t2h(t)=112 t-16 t^{2}h(t)=112t−16t2. After how long will it reach its maximum height?Do not round your answer.Time: □\square□ seconds

Problem 2151

Problem 2152

C. sin⁡π8\sin \frac{\pi}{8}sin8π​

Problem 2153

Problem 2154

Problem 2155

Fill in the table using this function rule. $y=-10 x+2$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-1 & $\square$ \\ \hline 0 & $\square$ \\ \hline 1 & $\square$ \\ \hline 5 & $\square$ \\ \hline \end{tabular}

Bestimme die lineare Funktionsgleichung, a) $m=2 ; P(-1 \mid-5)$

Consider the following functions. $f(x)=x^{2}-3 \text { and } g(x)=x-3$
Step 1 of 2: Find the formula for $(\mathrm{f} \cdot \mathrm{g})(\mathrm{x})$ and simplify your answer.

9. Use an appropriate substitution to evaluate the definite integral $\int_{2}^{6} \frac{x}{\sqrt{2 x-3}} d x$ .

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of -6 and 2 , and goes to $-\infty$ as $x \rightarrow-\infty$ .
Answer

(VCAA-type question) The rule connecting $y$ and $x$ as shown in the graph is: A $y=2 x$ B $y=2 x^{2}$ c $y=2 \sqrt{x}$ D $y=\frac{1}{2} x$ E $y=x^{2}+2$

The graph of $y=x^{2}$ is the solid black graph below. Which function represents the dotted graph?

Tides in a specific location can be approximated using the periodic function shown on the graph.
What is the interpretation of the amplitude in this application?

Consider the function $y=2^{-x}+3$ a) Find the $y$ -value of the $y$ -intercept of the curve $y=2^{-x}+3$ . $y=4$ ...
Find the equation of the horizontal asymptote of the curve $y=2^{-x}+3$ Enter your next step here

$\begin{array}{l}f(x)=10 \sqrt{95+x} \\ f(49)=\square\end{array}$

$\begin{array}{l}f(x)=(4-x)^{2} \\ f(11)=\square\end{array}$

(1 point) Let $f(x)=(\ln (x))^{\operatorname{sed}(x)}$ . Find $f^{\prime}(x)$ . $f^{\prime}(x)=$

$\begin{array}{l}f(x)=7 \sqrt{x-155} \\ f(159)=\end{array}$

$\begin{array}{l}f(x)=(1+x)^{2} \\ f(9)=\square\end{array}$

$\begin{array}{l}f(r)=r^{2} \\ f(d-6)=\end{array}$

$\begin{array}{l}f(y)=y^{2}-10 y \\ f(s+2)=\end{array}$

2) $\sin X$

نعثر الدالة $f$ المعر فلة على

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=48 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

5. Find $\frac{d^{2} y}{d x^{2}}$ for $y=\frac{x+3}{x-1}$ (a) 0 (b) $\frac{-8}{(x-1)^{3}}$ (c) $\frac{-4}{(x-1)^{3}}$ (d) $\frac{8}{(x-1)^{3}}$ (e) None of these

8. Find $y^{\prime}$ if $y=\sin (x+y)$ . (a) 0 (b) $\frac{\cos (x+y)}{1-\cos (x+y)}$ (c) $\cos (x+y)$ (d) 1 (c) None of these

A ball is thrown vertically upward. After $t$ seconds, its height $h$ (in feet) is given by the function $h(t)=112 t-16 t^{2}$ . After how long will it reach its maximum height?
Do not round your answer.
Time: $\square$ seconds

C. $\sin \frac{\pi}{8}$

Problem 5. Use the change-of-base theorem to write each logarithm (i) in terms of common logarithms, (ii) in terms of natural logarithms. Approximation the answer to four decimal places for each logarithm. (a) $\log _{4} 20$ (b) $\log _{2} 0.7$

Which is the graph of $y=\cos (x)+3$ ?

points) $f(x)=\sin (\sin (x))$ then $f^{\prime}(x)=\square$ Preview My Answers Submit Answers

Which of the following functions has a graph that is symmetric about the $y$ -axis?
Select all that apply. A. $y=\frac{1}{x}$ B. $y=\sqrt{x}$ C. $y=|x|$ D. $y=x^{3}$

2. find the zeres and verten for the function $f(x)=3 x^{2}+12 x-135$

Suppose that $f(x)=(5-\ln (x))^{3}$ . Find $f^{\prime}(1)$ . $f^{\prime}(1)=$

Use synthetic division and the remainder theorem to find $P(a)$ . $\begin{array}{l} P(x)=x^{3}+6 x^{2}-7 x+6 ; a=3 \\ P(a)=\square \end{array}$ $\square$ (Simplify your answer.)

Suppose that $f(x)=\frac{3}{\ln \left(x^{2}+2\right)}$
Find $f^{\prime}(1)$ . $f^{\prime}(1)=$

If $f(x)=(5 x+4)^{-1}$
Find $f^{\prime}(x)$ . Then $f^{\prime}(x)=$ $\square$ Find $f^{\prime}(3)$ . Then $f^{\prime}(3)=$ $\square$

(1 point) Let $f(x)=e^{-7 x^{2}}$ . Then $f(x)$ has a relative minimum at $x=$ a relative maximum at $x=\square$ and inflection points at $x=\square$ and at $x=\square$
Write DNE if any of the above do not exist. Write the inflection points (if ar