Browse Function problems Studdy Solved!

Problem 2301

3. Given sec $x=\frac{\sqrt{10}}{3}$ , where $\frac{3 \pi}{2} \leq x \leq 2 \pi$ , determine the value of $\cos (2 x)$ (u) $\frac{1}{19}$ B) $-\frac{37}{19}$ C) $\frac{37}{19}$
4. What is the exact value of $\sin \frac{13 \pi}{12}$ ? D) $-\frac{1}{19}$ A) $\frac{\sqrt{6}+\sqrt{2}}{4}$ B) $\frac{\sqrt{6}-\sqrt{2}}{4}$ C) $\frac{\sqrt{2}-\sqrt{6}}{4}$ D) $\frac{\sqrt{2}-\sqrt{3}}{2}$

See Solution

Problem 2302

7. [0.6/1 Points] DETAILS MY NOTES SCALCET9 4.7.065. PREVIOUS ANSWERS ASK YOUR TEACHE
If $C(x)$ is the cost of producing $x$ units of a commodity, then the average cost per unit is $c(x)=\frac{C(x)}{x}$ . Consider the cost function $C(x)$ given below. (Round your answers to the nearest cent.) $C(x)=54,000+140 x+4 x^{3 / 2}$ (a) Find the total cost (in dollars) at a production level of 1,000 units. \ $320,491.11$ \square $(b) Find the average cost (in dollars per unit) at a production level of 1,000 units. \$$ \square $320.49$ \checkmark $per unit (c) Find the marginal cost (in dollars per unit) at a production level of 1,000 units. \$$ \square $329.74 - per unit (d) Find the production level (in units) that will minimize the average cost.$ \square $units (e) What is the minimum average cost (in dollars per unit)? \$$ \square$ per unit

See Solution

Problem 2303

A ferris wheel is 35 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function $h=f(t)$ gives your height in meters above the ground $t$ minutes after the wheel begins to turn.
What is the Amplitude? $\square$ meters
What is the Midline? $\mathrm{y}=$ $\square$ meters
What is the Period? $\square$ minutes
How High are you off of the ground after 4 minutes? $\square$ meters

See Solution

Problem 2304

Evaluate the expression $\cos ^{-1}\left(\sin \left(\frac{\pi}{3}\right)\right)$ .
Give your answer as an exact value

See Solution

Problem 2305

(20) 1. Una empresa está disen̄ando un depósito de agua con forma de sólido de revolución. La región utilizada para ello está acotada entre las funciones: $f(x)=-x^{2}+2 \quad \text { y } g(x)=x$ donde $x$ se mide en metros y cada una de las funciones en metros cuadrados. Es importante mencionar que dicha región va a girar alrededor de la recta $x=1$ . (10) (a) Determine el área de la región acotada que se usará para generar el sólido de revolución. (10). (b) Explique si dicho sólido puede tener un volumen mínimo de $10 \pi \mathrm{~m}^{3}$ .

See Solution

Problem 2306

Find the intervals where the function $f(x) = \frac{1}{2} x^4 - 4x^2 + 7$ is concave upward.

See Solution

Problem 2307

Find the exact value of $\sin \pi$ . $\sin \pi=$

See Solution

Problem 2308

(20) 2. En un ejercicio de clase, tres estudiantes, Ana, Luis y Marta, deciden calcular la integral de la función $f(x)=\frac{2 x}{1+x^{2}} \text { en el intervalo }(0,1)$
Cada estudiante elige una estrategia distinta: - Ana utiliza un método de integración para determinar el valor exacto de la integral. - Luis emplea una aproximación numérica basada en el método del trapecio, dividiendo el intervalo en 2 subintervalos iguales. - Marta genera la serie de potencias de $f(x)$ alrededor de $x=0 \mathrm{y}$ , utilizando un polinomio de grado 3, aproxima el valor de la integral en el intervalo.
Por tanto, (a) Calcula el valor de la integral utilizando la estrategia de Ana. (b) Estima el valor de la integral utilizando la estrategia de Luis. (c) Aproxima el valor de la integral utilizando la estrategia de Marta. (d) Responde: ¿Quién, entre Luis y Marta, obtiene un resultado más cercano al valor calculado por Ana? Justifica tu respuesta.
Información que pueda interesar \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 0 & $\frac{1}{4}$ & $\frac{1}{2}$ & $\frac{3}{4}$ & 1 \\ \hline $f(x)=\frac{2 x}{1+x^{2}}$ & 0 & $\frac{8}{17}$ & $\frac{4}{5}$ & $\frac{24}{25}$ & 1 \\ \hline \end{tabular} $\begin{array}{l} \int_{0}^{1} \frac{2 x}{1+x^{2}} \\ \frac{2(1)}{1+(1)^{2}}-\frac{2(0)}{1+(0)^{2}} \\ \frac{13}{20} \ln (2) \end{array}$ $\overbrace{}^{\frac{1}{4} \quad \frac{13}{40}} \quad \frac{1}{2} \ln (2) \quad \underbrace{\frac{1}{2}} \quad \frac{13}{20} \ln (2)$

See Solution

Problem 2309

Suppose that the functions $g$ and $f$ are defined as follows. $\begin{array}{l} g(x)=-4+3 x^{2} \\ f(x)=4-8 x \end{array}$ (a) Find $\left(\frac{g}{f}\right)(-5)$ . (b) Find all values that are NOT in the domain of $\frac{g}{f}$ .
If there is more than one value, separate them with commas. (a) $\left(\frac{g}{f}\right)(-5)=$ !i. (b) Value(s) that are NOT in the domain of $\frac{g}{f}$ :

See Solution

Problem 2310

Let $\theta$ be an angle in quadrant I such that $\sin \theta=\frac{7}{10}$ . Find the exact values of $\sec \theta$ and $\tan \theta$ .

See Solution

Problem 2311

Given the values of the derivative $f^{\prime}(x)$ in the table and that $f(0)=150$ , find or estimate $f(x)$ for $x=0,2,4,6$ . \begin{tabular}{|c|c|c|c|c|} \hline $x$ & 0 & 2 & 4 & 6 \\ \hline $f^{\prime}(x)$ & 13 & 28 & 43 & 55 \\ \hline $f(x)$ & $\square$ & & & $\square$ \\ \hline \end{tabular}

See Solution

Problem 2312

The graph of a function $g$ is shown below. Find $g(2)$ and find one value of $x$ for which $g(x)=4$ . (a) $g(2)=$ $\square$ (b) One value of $x$ for which $g(x)=4$ : $\square$

See Solution

Problem 2313

The graph of a function $h$ is shown below. Find one value of $x$ for which $h(x)=1$ and find $h(-2)$ . (a) One value of $x$ for which $h(x)=1$ : $\square$ (b) $h(-2)=$ $\square$

See Solution

Problem 2314

Finding inputs and outputs of a function from its graph
The graph of a function $h$ is shown below. Find $h(-2)$ and find one value of $x$ for which $h(x)=-1$ . (a) $h(-2)=3$ (b) One value of $x$ for which $h(x)=-1$ : $\square$

See Solution

Problem 2315

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 75 degrees at midnight and the high and low temperature during the day are 91 and 59 degrees, respectively. Assuming $t$ is the number of hours since midnight, find an equation for the temperature, $D$ , in terms of t . $D(t)=$ $\square$

See Solution

Problem 2316

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 80 and 50 degrees, respectively. Assuming $t$ is the nulnber of hours since midnight, find an equation for the temperature, $D$ , in terms of $t$ . $D(t)=$ $\square$

See Solution

Problem 2317

Find the following derivative: ( 1 Mark) $f(x)=8 x^{3}-\frac{4}{x^{4}} x-12 x-0.1$

See Solution

Problem 2318

340 [EX1] (1) Find the amplitude, period, phase shift, and (2) Graph two periods of each function. (1) $y=2 \sin (2 x+\pi)+2$

See Solution

Problem 2319

Q32) $\lim _{x \rightarrow 1} \frac{\sin (1-\sqrt{x})}{x-1}$ ? a) $-\frac{1}{2}$ b) $1 / 2$

See Solution

Problem 2320

tion de la tangente à la courbe représentative de $f$ au point d'abscisse a. $f(x)=-x^{2}+2 x-8 ; a=-2$

See Solution

Problem 2321

$\lim _{x \rightarrow 2} \frac{x^{3}-2 x^{2}}{x^{2}-5 x+6}$

See Solution

Problem 2322

Determination de tangentes Pour les exercices 665 à G2\ $, déterminez une équation de la tangente à la courbe représentative de$ f $au point d'abscisse$ a$.
67 数 $f(x)=\frac{x+3}{1-2 x} ; a=-1$ .

See Solution

Problem 2323

A bank features a savings account that has an annual percentage rate of $r=3.9 \%$ with interest compounded quarterly. Bryan deposits $\$ 9,000$ into the account.
The account balance can be modeled by the exponential formula $S(t)=P\left(1+\frac{r}{n}\right)^{n t}$ , where $S$ is the future value, $P$ is the present value, $r$ is the annual percentage rate written as a decimal, $n$ is the number of times each year that the interest is compounded, and $t$ is the time in years. (A) What values should be used for $P, r$ , and $n$ ? $P=$ $\square$ $r=$ $\square$ $n=$ $\square$ 4 (B) How much money will Bryan have in the account in 8 years?
Answer = \\square$ Round answer to the nearest penny.

See Solution

Problem 2324

Given the function $f(x)=\left\{\begin{array}{ll} 5 x+7 & x<0 \\ 5 x+14 & x \geq 0 \end{array}\right.$
Calculate the following values: $\begin{array}{l} f(-1)=\square \\ f(0)=\square \\ f(2)=\square \end{array}$

See Solution

Problem 2325

find $L^{-1}\left\{\frac{s^{2}-40 s-393}{(s-11)\left(s^{2}+4 s+13\right)}\right\}$

See Solution

Problem 2326

5) $f(x)=\frac{x^{3}+x^{2}-2 x}{-3 x^{2}+6 x}$

See Solution

Problem 2327

30 1. $f(x)=(3 x+1)^{3} ; \mathrm{I}=\mathbb{R}$
2. $f(x)=(1-2 x)^{4} ; I=\mathbb{R}$
3. $f(x)=\sqrt{2 x+1} ; I=\left[\frac{-1}{2} ;+\infty[\right.$
4. $\left.f(x)=\sqrt{2-3 x} ; I=]-\infty ; \frac{2}{3}\right]$

See Solution

Problem 2328

1 - 2

See Solution

Problem 2329

1. The South Bowie Library and Oxon Hill Library are having a used book sale. The total cost, $y$ , is a function of the number of books, $x$ .
Which function has a greater constant rate of change? Explain. How much cheaper or more expensive is South Bowie Library than Oxon Hill Library? Explain.

See Solution

Problem 2330

Question 3 5 pts
A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $\$ 3$ per foot. The material for the fourth side costs $\$ 9$ per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.
The short side is $\qquad$ ft and the long side is $\qquad$ ft. The short side is 25 ft and the long side is 50 ft . The short side is 10 ft and the long side is 125 ft . The short side is 75 ft and the long side is 450 ft . The short side is 5 ft and the long side is 250 ft .

See Solution

Problem 2331

Question 3 of 20 This test: 100 point(S) poss This question: 5 point(s) p
Let $F(x)=x^{2}-4$ and $G(x)=3-x$ $(F / G)(x)=$ $\square$ Find $(F / G)(x)$ .

See Solution

Problem 2332

20. State which of the following quadratic functions is in standard form and which is in vertex form. Then find the coordinates of the vertex for each one. A) $s(x)=-(x+5)^{2}-8$ B) $g(x)=-4+3 x-2 x^{2}$

See Solution

Problem 2333

21. You have a 1200 -foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What is the maximum area and the dimensions of this largest rectangular enclosure? \begin{tabular}{|l|l|} \hline $\square$ \\ $\square$ \end{tabular}

See Solution

Problem 2334

(a) $\lim _{x \rightarrow-1^{+}} f(x)=1$ True (b) $\lim _{x \rightarrow 2} f(x)$ does not exis (c) $\lim _{x \rightarrow 2} f(x)=2$ Tru八 (d) $\lim _{x \rightarrow 1^{-}} f(x)=2$ Fal (e) $\lim _{x \rightarrow 1^{+}} f(x)=1$ imu (f) $\lim _{x \rightarrow 1} f(x)$ does not ex (g) $\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0^{-}} f(x)$ TMu

See Solution

Problem 2335

The function $f(x)=3 x+5 x^{-1}$ has one local minimum and one local maximum. This function has a local maximum at $x=$ with value and a local minimum at $x=$ $\square$ with value $\square$

See Solution

Problem 2336

Consider the following program: What output is generate program is executed? public static void main(String args[]) i Notes $n=$ new $\operatorname{Notes}(5,3)$ ; int $y=0$ ; int $x=n$ .function $A(y)$ ; System.out.print $1 n(" y="+y)$ ; \} *Use the following Notes class to answer. ``` public class Notes { private int myNum; private int myValue; public Notes(int x, int y) { myNum = x; myValue = y; } public int functionA(int y) { myNum += y; y++; return y + 1; } ```

See Solution

Problem 2337

1. Write a third degree polynomial function with integer coefficients that has zeroes $x=1$ and $x=i \sqrt{2}$ . [You may not leave the function in factored form.]

See Solution

Problem 2338

The following program is to read College name, a number of students and tuition from the file "colleges.txt" and print the College name, the number of students and tuition. Select the correct option to replace the missing code. public class ScannerStuff \{ public static void main(String[] args) \{ try \{ Scanner input $=$ new $\operatorname{Scanner}$ (new File("colleges .txt")); while (input hasNext()) \{ String name $=/^{}$ missing code $\mathrm{A}^{} /$ ; int numstu $=/ $ missing code $\mathrm{B}^{} /$ ; int tuition = input. nextInt(); input. nextLine();
System. out. println(name $+\cdots n+$ numStu $+\cdots+$ tuition); $\}$ ) catch(IOException e) ( System.out.println(); \} ) )
Option 1: A: input. next() B: input. next()
Option 2: A: input. nextint() B : input. nextInt()
Option 3: A: input. nextline() B: input. nextint()

See Solution

Problem 2339

FRQ 4.1 and 4.2
There are 700 people in line for a popular amusement-park ride when the ride begins operation in the morning. Once it begins operation, the ride accepts passengers until the park closes 8 hours later. While there is a line, people move onto the ride at a rate of 800 people per hour. The graph above shows the rate, $r(t)$ , at which people arrive at the ride throughout the day. Time $t$ is measured in hours from the time the ride begins operation.
1. Is the number of people waiting in line to get on the ride increasing or decreasing between $t=2$ and $t=3$ ? Justify your answer.

See Solution

Problem 2340

Delow is the function $f(x)$ .
Over which interval of $x$ values is $f^{\prime}>0$ ? $(3, \infty)$ $[3, \infty)$ $(-\infty, 3)$ $(-\infty, 3]$ $(-\infty, \infty]$
Over which interval of $x$ values is $f^{\prime}<0$ ? $(3, \infty)$ $[3, \infty)$ $(-\infty, 3)$ $(-\infty, 3]$ $(-\infty, \infty]$
Over the interval $(-\infty, \infty)$ , this function is concave up ( $f^{\prime \prime}>0$ ) concave down ( $f^{\prime \prime \prime}<\mathbf{0}$ )

See Solution

Problem 2341

1. The point where the graph of a function crosses the $x$ -axis is called the $\qquad$
2. To find the $x$ -intercept, set $\qquad$ to zero and solve for x .
3. The point where the graph of a function crosses the $y$ -axis is called the $\qquad$ .
4. To find the $y$ -intercept, set $\qquad$ to zero and solve for $y$ .

See Solution

Problem 2342

25. If point $\left(\frac{-2}{3}, \frac{-1}{4}\right)$ lies on the graph of the rational function $f(x)=\frac{6 x+3}{x+\frac{14}{3}} f(x)$ , then which point lies on the graph of the multiplicative inverse, or reciprocal, function of function $f(x)$ ?

See Solution

Problem 2343

Drill Problem 5.7 Consider a continuous-time signal defined by $g(t)=\frac{\sin (\pi t)}{\pi t}$
The signal $g(t)$ is uniformly sampled to produce the infinite sequence $\left\{g\left(n T_{s}\right)\right\}_{n=-\infty}^{\infty}$ . Determine the condition that the sampling period $T_{s}$ must satisfy so that the signal $g(t)$ is uniquely recovered from the sequence $\left\{g\left(n T_{s}\right)\right\}$ .

See Solution

Problem 2344

The loan amount is a function of time and can be represented by the line of best fit $y=15,413-1,635 x$ , where $x$ is the number of years. How much is left on the loan after 9 years? (1 point)
The loan amount is $\$$ $\qquad$ after 9 years.

See Solution

Problem 2345

Consider the function $f(x)=x^{2} e^{6 x}$ . $f(x)$ has two inflection points at $x=C$ and $x=D$ with $C<D$ where $C$ is $\square$ and $D$ is $\square$ Finally for each of the following intervals, tell whether $f(x)$ is concave up or concave down. $(-\infty, C)$ : Select an answer $\checkmark$ $(C, D)$ : Select an answer $\checkmark$ $(D, \infty)$ Select an answer $\checkmark$ Question Help: Video

See Solution

Problem 2346

Question 2 of 10 What are the zeros of this function? A. $x=0$ and $x=-6$ B. $x=0$ and $x=-9$ C. $x=3$ and $x=-9$ D. $x=0$ and $x=6$

See Solution

Problem 2347

Question 2 of 10, Step 1 of 1 1/10 Correct 2
The marginal profit for a certain style of purse is given by $P^{\prime}(x)=38-0.86 x$ dollars per purse, where $x$ is the number of purses produced and sold weekly. Find the profit for the first 49 purses that are produced and sold. Round your answer to the nearest cent.
Answer Tables Keypad Keyboard Shortcuts

See Solution

Problem 2348

a. Write the cost function. $C(x)=$ $\square$ (Type an expression using $x$ as the variable.) b. Write the revenue function. $R(x)=$ $\square$ (Type an expression using $x$ as the variable.) c. Determine the break-even point. (Type an ordered pair. Do not use commas in large numbers.) This means that when the company produces and sells the break-even number of canoes A. the money coming in equals the money going out B. there is less money coming in than going out. C. there is more money coming in than going out. D. there is not enough information.

See Solution

Problem 2349

pondus Monitor Question 7, 4.4.56 Test Score: $75.2 \%, 75.2$ of 100 points Points: 7.2 of 12 Close
Use the derivative $f^{\prime}(x)=(x-2)(x+2)(x+4)$ to determine the local maxima and minima of $f$ and the intervals of increase and decrease. Sketch a possible graph of $f(f$ is not unique).
The local maximum/maxima is/are at $x=-2$ . (Use a comma to separate answers as needed.) The local minimum/minima is/are at $x=-4,2$ . (Use a comma to separate answers as needed.) The interval(s) of increase is(are) $(-4,-2),(2, \infty)$ . (Type your answer in interval notation. Use a comma to separate answers as needed.) The interval(s) of decrease is(are) $(-\infty,-4),(-2,2)$ . (Type your answer in interval notation. Use a comma to separate answers as needed.) Which is a possible graph of $f$ ? A. B. c. D.

See Solution

Problem 2350

1. La lune est toujours à moitié illuminée par le soleil. La partie de lune que nous observons dépend sur la position de la lune en orbite autour du soleil. Le tableau suivant démontre quelle portion de la lune est visible en Ontario du jour 1 à jour 74 de l'année 2006. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline Jour & 1 & 1 & $4 / /$ & $7 /$ & 10 & 14 & 20 & 24 & 29 \\ 34 \\ \hline Portion & 0,02 & 0,22 & 0,55 & 0,83 & 1 & 0,73 & 0,34 & 0 & 0,28 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline Jour & 41 & 44 & 48 & 53 & 56 & 59 & 63 & 70 & 74 \\ \hline Portion & 0,92 & 1,00 & 0,86 & 0,41 & 0,12 & 0,00 & 0,23 & 0,88 & 1,00 \\ \hline \end{tabular} a. Déterminer une équation sinusoïdale qui modélise la portion visible de la lune en fonction du temps. b. Déterminer le domaine et l'image de la fonction, pour une année. c. Utiliser l'équation pour prédire toutes les journées de l'année, quand la portion visible de la lune sera à $40 \%$ .

See Solution

Problem 2351

Find the total area bounded by the $x$ -axis and the curve $y=f(x)$ on the indicated interval. Enter your answer in exact form or as a decimal number rounded to the nearest thousandth. $f(x)=2 \sqrt{7 x-8} ;[3,5]$
Answer Tables Keypad Keyboard Shortcuts Submit Answer

See Solution

Problem 2352

7. Given $f(x)=\frac{9}{5} x+32$ , find the following. a. $f(60)$ b. $f(0)$ c. $f(25)$

See Solution

Problem 2353

Answer the questions below. \begin{tabular}{|l|l|} \hline (a) Weight loss is affected by the number of calories taken in: the fewer calories taken \\ in, the more weight lost. Which is the dependent variable? \end{tabular}

See Solution

Problem 2354

B. What is the direction of variation of each of the following functions: (co be done by students) 1) $f(x)=\cos x$ for $0 \leq x$ 2) $g(x) \frac{x^{2}+1}{x-1}$ on its domath of definition 3) $h(x)=\sqrt{x}$ on lits domain of definition

See Solution

Problem 2355

If $f(x)=4 x-12$ , what is $f(2) ?$ A. -4 B. 4 C. -20 D. 8

See Solution

Problem 2356

The speed of a car traveling on a highway is being recorded once per second for two minutes. During this time interval, the car gradually speeds up slightly to pass another vehicle, then the car returns to its original speed. The recorded speed of the car with respect to time can be modeled by linear, quadratic, and exponential functions. For each of the three models, their residuals are small and are without pattern. Which of the following conclusions is best? (A) A linear model is best based on contextual clues. (B) A quadratic model is best based on contextual clues. (C) An exponential model is best based on contextual clues. (D) Contextual clues fail to help in selecting a model for this contextual situation.

See Solution

Problem 2357

Put the quadratic into vertex form and state the coordinates of the vertex. $y=x^{2}-6 x+21$

See Solution

Problem 2358

Given the function $f(x)=\frac{-x^{2}+9 x-14}{x^{2}-7 x}$ , find any removable discontinuities, and vertical and horizontal asymptotes, if they exist. If there is more than one, list the numbers from least to greatest, separated by a comma.
Removable discontinuity at $x=$ $\square$ Vertical Asymptote at $x=$ $\square$ Horizontal Asymptote at $y=$ $\square$

See Solution

Problem 2359

3. The graph of which of the following functions in the $x y$ -plane has at least one $x$ -intercept, at least one hole, at least one vertical isf motote, and a horizontal asymptote. $f(x)=\frac{x^{2}-1}{x^{2}-x-30}$ Q. $f(x)=\frac{x^{2}-1}{x^{3}-x-6}$ 0. $f(x)=\frac{x^{2}-16}{x^{2}-x-6}$ Previous 1 () () 3 ® 4 0 5 (3) 6 () 7 0 8 . 10

See Solution

Problem 2360

2) The fox population in a certain region has an annual growth rate of 8 percent per year. (Note: Foxes mate once per year.) It is estimated that the fox population in the year 2020 was 13500. (a) Find a function that models the fox population $t$ years after 2020 (Note: $t=0$ for 2020 ).
The function is $P(t)=$ $\qquad$ (b) Use the function from part (a) to estimate the fox population in the year 2028. (The answer should be an integer.) There will be $\qquad$ foxes in the year 2028.

See Solution

Problem 2361

Select all intervals in which a real zero is located for the function $f(x)=x^{4}-2 x^{3}+3 x^{2}-5$ A) $x=-2$ and $x=-1$ B) $x=-1$ and $x=0$ c) $x=0$ and $x=1$ D) $x=1$ and $x=2$ E) $x=2$ and $x=3$ F) $x=3$ and $x=4$

See Solution

Problem 2362

Question 1 (1 point) In the $x y$ -plane, the point $(8,10)$ lies on the graph of the function $y=f(x)$ . Which of the following points must lie on the graph of the function $y=2 f(x-3)+5 \text { ? }$ $(11,15)$ $(5,15)$ $(5,10)$ $(5,25)$ $(11,25)$

See Solution

Problem 2363

10) Let $f(x)=\left(\frac{1}{6}\right)^{x}$ . Find $f(-2)$ . A) $\frac{1}{36}$ B) $-\frac{1}{36}$ C) -12 D) 36

See Solution

Problem 2364

The plot of what function appears below? $f(x)=x^{2}$ $f(x)=-(x-1)^{2}$ $f(x)=-x^{2}+1$ $f(x)=-(x+1)^{2}$ $f(x)=(x-1)^{2}$

See Solution

Problem 2365

Use the table of values of the function $f(x)=-x^{4}+5 x^{3}-7 x+9$ to complete the sentences.
A relative minima is located near $x=5$ A relative maxima is located near Select Choice

See Solution

Problem 2366

Question Watch Video Show Examples
Which of the following regressions represents the weakest linear relationship between x and y ? \begin{tabular}{llll} Regression 1 & Regression 2 & Regression 3 & Regression 4 \\ \hline $y=a x+b$ & $y=a x+b$ & $y=a x+b$ & $y=a x+b$ \\ $a=-19.4$ & $a=5.8$ & $a=-19.5$ & $a=6.9$ \\ $b=17.7$ & $b=16.7$ & $b=-0.6$ & $b=13.4$ \\ $r=-0.7037$ & $r=0.3984$ & $r=-0.296$ & $r=0.2412$ \end{tabular}
Answer Regression 1 Regression 2 Submit Answer Regression 3 Regression 4

See Solution

Problem 2367

Give the equation of the vertical asymptote of the function $f(x)=\log (x-3)$ $\square$ Give domain of the function $f(x)=\log (x-3)$ $\square$ $\square$ Calculator

See Solution

Problem 2368

If a 60 year-old buys a $\$ 1000$ life insurance policy at a cost of $\$ 80$ and has a probability of 0.914 of living to age 61 , find the expectation of the policy until the person reaches 61 . Round your answer to the nearest cent.
The expectation of the policy until the person reaches 61 is $\square$ dollars.

See Solution

Problem 2369

5 Sonya sells bracelets once a month at a flea market. The table shows her profits for a 5-month period.
Sonya \begin{tabular}{|l|c|c|c|c|c|} \hline Month & 1 & 2 & 3 & 4 & 5 \\ \hline Total Profit (\) & 30 & 60 & 90 & 120 & 150 \\ \hline \end{tabular} a. Kirsten sells bracelets once a month at a different flea market. The rate of change for her profits is \ $10$ per month. Complete the table and the graph to show her total profits.
Kirsten \begin{tabular}{|l|c|c|c|c|c|} \hline Month & 1 & 2 & 3 & 4 & 5 \\ \hline Total Profit (\$) & 10 & & & & \\ \hline \end{tabular}
Kirsten b. Sonya says that her profit is increasing 4 times as fast as Kirsten's profit. Do you agree? Explain. $\qquad$ $\qquad$ $\qquad$ Lesson 10 Compare Functions @Curriculum Associates, LLC Copying is not permitted. Downloaded by K. Hill at Alexandria - Monroe Junior Senior High Schaol. This resource expires on 6/30/2025.

See Solution

Problem 2370

Factor $f(x)$ into linear factors given that $k$ is a zero of $f(x)$ . 7) $f(x)=x^{3}-48 x-128 ; k=-4$ (multiplicity 2)

See Solution

Problem 2371

Example Compare the rates of change for these two functions. Which function has a greater rate of change?
Sarah's Savings $\frac{\text { vertical change }}{\text { horizontal change }}=\frac{6}{1}=6$
Alyssa's Savings $\frac{\text { vertical change }}{\text { horizontal change }}=\frac{8}{1}=8$
Alyssa's rate of change is greater than Sarah's.
1 What do the rates of change in the example represent? $\qquad$ $\qquad$

See Solution

Problem 2372

J Test Booklet
FRQ 4.1 and 4.2 hegafice (gany buck herve) Caren rides her bicycle along a straight road from home to school, starting at home at time $t=0$ minutes and arriving at school at time $t=12$ minutes. During the time interval $0 \leq t \leq 12$ minutes, her velocity $v(t)$ , in miles per minute, is modeled by the piecewise-linear function whose graph is shown above.
2. Shortly after leaving home, Caren realizes she left her calculus homework at home, and she returns to get it. At what time does she turn around to go back home? Give a reason for your answer. Canen turns aroun I to go hame at $t=2$ minutes beracde at theat tiphe we can see that her nelocity deereazes arich cun mean she went back hone. A particle moves along a straight line. For $0 \leq t \leq 5$ , the velocity of the particle is given by $v(t)=-2+\left(t^{2}+3 t\right)^{6 / 5}-t^{3}$ , and the $\begin{array}{l} \text { position of the particle is given by } s(t) \text {. It is known that } s(0)=10 . \quad-2+\left(t^{2}+3 t\right)^{6 / 5}-1^{3}=2 \\ v(t)=-2 \\ -2+\left(t^{2}+3 t\right)^{6 / 5}-t^{3}=-2 \\ \left.\left(t^{2}+3 t\right)^{6 / 5}-t^{3}=0 \quad\left(t^{2}+3 t\right)^{6 / s}=t^{3} \quad-3 t\right)^{6 / 5}-t^{3}=4 \end{array}$
3. 国 Find all values of $t$ in the interval $2 \leq t \leq 4$ for which the speed of the particle is 2 . $|V(t)|=2$ in the interval $2 \leq t \leq y$ are $t \approx 2.80$ and $t \approx 3.292$ . $a(t)=v(t)=-\sin \left(\frac{t^{2}}{2}\right)-(t+1) \cos \left(\frac{t^{2}}{2}\right) \cdot t$
A particle moves along the $x$ -axis so that its velocity at time $t$ is given by $a(t)=-\sin \left(\frac{t^{2}}{2}\right)-t(t+1) \cos \left(\frac{t^{2}}{2}\right)$ $\begin{array}{l} v(t)=-(t+1) \sin \left(\frac{t^{2}}{2}\right), a(2)=-\sin \left(\frac{2^{2}}{2}\right)-2(2-1) \cos \left(\frac{z^{2}}{2}\right) \\ v(2)=-(2+1) \sin \left(\frac{2^{2}}{2}\right)=-3 \sin (2)=-\sin (2)-6 \cos (2) \end{array}$
At time $t=0$ , the particle is at position $x=1$ .
4. 园 Find the acceleration of the particle at time $t=2$ . Is the speed of the particle increasing at $t=2$ ? Why or why not? The ucueteration at $y=2$ is Page 2 of 2 AP Calculus AB

See Solution

Problem 2373

Determine the intervals over which the function $d(x) = -x^2 + 2x - 1$ is decreasing.

See Solution

Problem 2374

Use the functions below to find the equation for the indicated operations. $f(x)=x^{2}-2 x-3 \quad g(x)=\frac{x-3}{2 x+3} \quad h(x)=3 x-4$
6. $g(h(x))$

See Solution

Problem 2375

Example Compare the rates of change for these two functions. Which function has a greater rate of change?
Sarah's Savings $\frac{\text { vertical change }}{\text { horizontal change }}=\frac{6}{1}=6$
Alyssa's Savings
Alyssa's rate of change is greater than Sarah's.
1 What do the rates of change in the example represent? The speed that they go up $\frac{\text { vertical change }}{\text { horizontal change }}=\frac{8}{1}=8$

See Solution

Problem 2376

For each function $h$ , find functions $f$ and $g$ so that $h(x)=(f \circ g)(x)$ .
10. $h(x)=\left|x^{5}-3\right|$

See Solution

Problem 2377

For each function $h$ , find functions $f$ and $g$ so that $h(x)=(f \circ g)(x)$ . 10. (5)
12. $h(x)=\left(x^{2}+1\right)^{2}$

See Solution

Problem 2378

Use the Trapezoidal Rule to approximate $\int_{-0.9}^{1.5} \frac{\tan x}{x+6} \mathrm{~d} x$ using $n=3$ . (Round your answer to 4 decimal places.)

See Solution

Problem 2379

Question Watch Video Show Examples
The function $f(t)=140(0.95)^{\frac{t}{7}}$ represents the change in a quantity over $t$ days. What does the constant 0.95 reveal about the rate of change of the quantity?
Answer Attempt 1 out of 2
The function is $\square$ exponentially at a rate of $\square$ \% every Submit Answer Copyrighte2024 DeltalMath com Aut rights peserved. PropeyPalicylIermsof Service

See Solution

Problem 2380

B. What is the direction of variation of each of the following functions: (co be done by students) 1) $f(x)=\cos x$ for $0 \leq x$ 2) $x(x) \frac{x^{3}+1}{x-1}$ on its domaln of definition 3) $h(x)=\sqrt{x}$ on its domain of definition

See Solution

Problem 2381

Find the vertical, horizontal, and oblique asymptotes, if any, of the following rational function. $Q(x)=\frac{5 x^{2}-29 x-6}{3 x^{2}-17 x-6}$
Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, $\square$ . (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is $\square$ and the rightmost asymptote is $\square$ . (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has no vertical asymptote.

See Solution

Problem 2382

Question Watch Video Show Examples
The function $f(t)=2200(0.9985)^{t}$ represents the change in a quantity over $t$ months. What does the constant 0.9985 reveal about the rate of change of the quantity?
Answer Attempt 1 out of 2
The function is exponentially at a rate of $\square$ \% every

See Solution

Problem 2383

Question 8 0/3 pts 3 19 Details
Find the domain of function $r(x)=\sqrt{x^{2}+5 x-24}$ . Write your answer using interval notation in the box below. Enter your values as integers or reduced fractions.
Domain of $r(x)=\sqrt{x^{2}+5 x-24}$ : $\square$ Question Help: Video Submit Question

See Solution

Problem 2384

sea suriace temperature in degress Calius ( C ) and the annual growith of a porilculor coral reel species in cenilmelers per year ( $\mathrm{cm} / \mathrm{year}$ ) of diferent localions in the Carbbean Sea. Some of the data they have recorded is shown In the fable below: \begin{tabular}{|l|l|l|ll|l|l|l|} \hline $x$ & \begin{tabular}{l} Average Sea Surface \\ Temperture ( C $)$ \end{tabular} & 26.7 & 26.6 & 26.6 & 26.5 & 26.3 & 26.1 \\ \hline \begin{tabular}{l} Grewth Rate \\ (cm/year) \end{tabular} & 0.85 & 0.85 & 0.79 & 0.86 & 0.89 & 0.92 \\ \hline \end{tabular}
Use Desmos to determine the linear regression equation. State the equation in slope intercept form: $\mathbf{y = m x + b}$ . Round parameters to the hundredths place. (5)

See Solution

Problem 2385

9. Determine the derivative of the following functions: $\begin{array}{ll} f(x)=\left(x^{2}+x+1\right)^{3} ; & f(x)=\sqrt{x}+\frac{1}{x} \\ f(x)=\frac{\sin \left(x^{3}+1\right)}{\cos (2 x+2)} ; & f(x)=\sin \left(\sqrt{x^{2}+1}\right) \\ f(x)=\operatorname{tg}\left(x^{2}\right) ; & f(x)=e^{x^{2} \sin x} \end{array}$

See Solution

Problem 2386

9. Determine the derivative of the following functions: $\begin{array}{ll} f(x)=\left(x^{2}+x+1\right)^{3} ; & f(x)=\sqrt{x}+\frac{1}{x} \\ f(x)=\frac{\sin \left(x^{3}+1\right)}{\cos (2 x+2)} ; & f(x)=\sin \left(\sqrt{x^{2}+1}\right) \\ f(x)=\operatorname{tg}\left(x^{2}\right) ; & f(x)=e^{x^{2} \sin x} \end{array}$

See Solution

Problem 2387

9. Determine the derivative of the following functions: $\begin{array}{ll} f(x)=\left(x^{2}+x+1\right)^{3} ; & f(x)=\sqrt{x}+\frac{1}{x} \\ f(x)=\frac{\sin \left(x^{3}+1\right)}{\cos (2 x+2)} ; & f(x)=\sin \left(\sqrt{x^{2}+1}\right) \\ f(x)=\operatorname{tg}\left(x^{2}\right) ; & f(x)=e^{x^{2} \sin x} \end{array}$

See Solution

Problem 2388

Let $f(x)=3 x-1$ and $g(x)=x^{2}+4$ Find $(f \circ g)(1)$
Then $(f \circ g)(1)=$ $\square$ (Simplify your answer.)

See Solution

Problem 2389

$y = \sqrt{x} + x^2 \quad \text{over} \quad [1,9]$
Find the value of the integral of $y$ over the interval $[1,9]$ using the Fundamental Theorem of Calculus, Part 2.

See Solution

Problem 2390

Which rule describes the function in the graph below? $\left[-\frac{1}{2} x, x \leq-2\right.$

See Solution

Problem 2391

Consider the following. (If an answer does not exist, enter DNE.) $f(x)=7 \sin (x)+7 \cos (x), \quad 0 \leq x \leq 2 \pi$ (a) Find the interval(s) on which $f$ is increasing. (Enter your answer using interval notation.) $\square$ (b) Find the interval(s) on which $f$ is decreasing. (Enter your answer using interval notation.) $\square$ (c) Find the local minimum and maximum values of $f$ . local minimum value $\square$ local maximum value $\square$

See Solution

Problem 2392

WeBWorK 5 - Topics 10 - 12: Problem 3 (1 point)
Consider the function $f(x)$ whose second derivative is $f^{\prime \prime}(x)=10 x+5 \sin (x)$ . If $f(0)=4$ and $f^{\prime}(0)=2$ , what is $f(x)$ ? Answer: $\square$

See Solution

Problem 2393

What is the first derivative of $p(x)=\ln \left(4 x^{3}+x^{2}+1\right)$ ?
Select the correct answer below: $\frac{12 x^{2}+2 x}{4 x^{3}+x^{2}+1}$ $\frac{4 x^{3}+x^{2}+1}{12 x^{2}+2 x}$ $\frac{1}{4 x^{3}+x^{2}+1}$ $\ln \left(12 x^{2}+2 x\right)$ $\frac{12 x^{2}+2 x}{\ln \left(4 x^{3}+x^{2}+1\right)}$

See Solution

Problem 2394

Consider the function shown. Does the function have an inverse that is also a function? Use the drop-down menus to explain. $y=\sqrt{x+4}, x \geq-4$
Click the arrows to choose an answer from each menu. The range of the function $y=\sqrt{x+4}, x \geq-4$ is Choose... For each input of the given domain of $y=\sqrt{x+4}$ , there Choose... $\square$ of the range. For this reason, the inverse of $y=\sqrt{x+4}, x \geq-4$ Choose... a function.

See Solution

Problem 2395

The function $f(x)$ is shown below. Is the inverse of $f(x)$ also a function? Use the drop-down menus to explain. $f(x)=2^{x}-3, \text { for all } x$
Click the arrows to choose an answer from each menu. The function $f(x)$ Choose... $\square$ every range value to exactly one domain value. The domain of $f(x)$ is Choose... $\square$ and the range of $f(x)$ is Choose... $\square$ . Therefore, the inverse of $f(x)$ is Choose...

See Solution

Problem 2396

What is the first derivative of $q(x)=\log _{5}\left(\frac{2 x^{2}+8}{x^{4} 5^{x}}\right) ?$
Select the correct answer below: $q^{\prime}(x)=\frac{4 x}{2 x^{2}+8}-\frac{4}{x}-1$ $q^{\prime}(x)=\frac{1}{\left(2 x^{2}+8\right) \ln 5}-\frac{4}{x \ln 5}-1$ $q^{\prime}(x)=\frac{4 x}{\left(2 x^{2}+8\right) \ln 5}-\frac{4}{x \ln 5}-1$ $q^{\prime}(x)=\frac{x^{4}(5) \ln 5}{2 x^{2}+8}$

See Solution

Problem 2397

Heather has 360 meters of fencing and wishes to enclose a rectangular field. Suppose that a side length (in meters) of the field is $x$ , as shown below. (a) Find a function that gives the area $A(x)$ of the field (in square meters) in terms of $x$ . $A(x)=$ $\square$ (b) What side length $x$ gives the maximum area that the field can have?
Side length $x$ : $\square$ meters (c) What is the maximum area that the field can have?
Maximum area: $\square$ square meters

See Solution

Problem 2398

Consider the equation below. (If an answer does not exist, enter DNE.) $f(x)=6 \cos ^{2}(x)-12 \sin (x), \quad 0 \leq x \leq 2 \pi$ (a) Find the interval on which $f$ is increasing. (Enter your answer using interval notation.) $\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$
Find the interval on which $f$ is decreasing. (Enter your answer using interval notation.) $\left(0, \frac{\pi}{2}\right) \cup\left(\frac{3 \pi}{2}, 2 \pi\right)$ (b) Find the local minimum and maximum values of $f$ . local minimum value $-12$ local maximum value 12 (c) Find the inflection points. (Order your answers from smallest to largest $x$ , then from smallest to largest $y$ .) $\begin{array}{l} (x, \sqrt{x})=(\square) \\ (x, y)=(\square) \end{array}$
Find the interval on which $f$ is concave up. (Enter your answer using interval notation.) $\square$ Find the interval on which $f$ is concave down. (Enter your answer using interval notation.) $\square$

See Solution

Problem 2399

The entire graph of the function $g$ is shown in the figure below. Write the domain and range of $g$ as intervals or unions of intervals. $\begin{array}{l} \text { domain }=\square \\ \text { range }=\square \end{array}$

See Solution

Problem 2400

Q9. Find the volume of the solid object having base in the $x y$ -plane bounded by the curves $y=x^{2}-1$ and $y=1-|x|$ (see image below) and having cross-sections perpendicular to the $x$ -axis that are squares.

See Solution

Function

Problem 2301

Problem 2302

Problem 2303

Problem 2304

Evaluate the expression cos⁡−1(sin⁡(π3))\cos ^{-1}\left(\sin \left(\frac{\pi}{3}\right)\right)cos−1(sin(3π​)).Give your answer as an exact value

Problem 2305

Problem 2306

Find the intervals where the function f(x)=12x4−4x2+7 f(x) = \frac{1}{2} x^4 - 4x^2 + 7 f(x)=21​x4−4x2+7 is concave upward.

Problem 2307

Find the exact value of sin⁡π\sin \pisinπ. sin⁡π=\sin \pi=sinπ=

Problem 2308

Problem 2309

Problem 2310

Let θ\thetaθ be an angle in quadrant I such that sin⁡θ=710\sin \theta=\frac{7}{10}sinθ=107​. Find the exact values of sec⁡θ\sec \thetasecθ and tan⁡θ\tan \thetatanθ.

Problem 2311

Problem 2312

The graph of a function ggg is shown below. Find g(2)g(2)g(2) and find one value of xxx for which g(x)=4g(x)=4g(x)=4. (a) g(2)=g(2)=g(2)= □\square□ (b) One value of xxx for which g(x)=4g(x)=4g(x)=4 : □\square□

Problem 2313

The graph of a function hhh is shown below. Find one value of xxx for which h(x)=1h(x)=1h(x)=1 and find h(−2)h(-2)h(−2). (a) One value of xxx for which h(x)=1h(x)=1h(x)=1 : □\square□ (b) h(−2)=h(-2)=h(−2)= □\square□

Problem 2314

Finding inputs and outputs of a function from its graphThe graph of a function hhh is shown below. Find h(−2)h(-2)h(−2) and find one value of xxx for which h(x)=−1h(x)=-1h(x)=−1. (a) h(−2)=3h(-2)=3h(−2)=3 (b) One value of xxx for which h(x)=−1h(x)=-1h(x)=−1 : □\square□

Problem 2315

Problem 2316

Problem 2317

Find the following derivative: ( 1 Mark) f(x)=8x3−4x4x−12x−0.1f(x)=8 x^{3}-\frac{4}{x^{4}} x-12 x-0.1f(x)=8x3−x44​x−12x−0.1

Problem 2318

340 [EX1] (1) Find the amplitude, period, phase shift, and (2) Graph two periods of each function. (1) y=2sin⁡(2x+π)+2y=2 \sin (2 x+\pi)+2y=2sin(2x+π)+2

Problem 2319

Q32) lim⁡x→1sin⁡(1−x)x−1\lim _{x \rightarrow 1} \frac{\sin (1-\sqrt{x})}{x-1}limx→1​x−1sin(1−x​)​ ? a) −12-\frac{1}{2}−21​ b) 1/21 / 21/2

Problem 2320

tion de la tangente à la courbe représentative de fff au point d'abscisse a. f(x)=−x2+2x−8;a=−2f(x)=-x^{2}+2 x-8 ; a=-2f(x)=−x2+2x−8;a=−2

Problem 2321

lim⁡x→2x3−2x2x2−5x+6\lim _{x \rightarrow 2} \frac{x^{3}-2 x^{2}}{x^{2}-5 x+6}limx→2​x2−5x+6x3−2x2​

Problem 2322

Problem 2323

Problem 2324

Problem 2325

find L−1{s2−40s−393(s−11)(s2+4s+13)}L^{-1}\left\{\frac{s^{2}-40 s-393}{(s-11)\left(s^{2}+4 s+13\right)}\right\}L−1{(s−11)(s2+4s+13)s2−40s−393​}

Problem 2326

5) f(x)=x3+x2−2x−3x2+6xf(x)=\frac{x^{3}+x^{2}-2 x}{-3 x^{2}+6 x}f(x)=−3x2+6xx3+x2−2x​

Problem 2327

Problem 2328

1 - 2

Problem 2329

1. The South Bowie Library and Oxon Hill Library are having a used book sale. The total cost, yyy, is a function of the number of books, xxx.Which function has a greater constant rate of change? Explain. How much cheaper or more expensive is South Bowie Library than Oxon Hill Library? Explain.

Problem 2330

Problem 2331

Question 3 of 20 This test: 100 point(S) poss This question: 5 point(s) pLet F(x)=x2−4F(x)=x^{2}-4F(x)=x2−4 and G(x)=3−xG(x)=3-xG(x)=3−x (F/G)(x)=(F / G)(x)=(F/G)(x)= □\square□ Find (F/G)(x)(F / G)(x)(F/G)(x).

Problem 2332

20. State which of the following quadratic functions is in standard form and which is in vertex form. Then find the coordinates of the vertex for each one. A) s(x)=−(x+5)2−8s(x)=-(x+5)^{2}-8s(x)=−(x+5)2−8 B) g(x)=−4+3x−2x2g(x)=-4+3 x-2 x^{2}g(x)=−4+3x−2x2

Problem 2333

21. You have a 1200 -foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What is the maximum area and the dimensions of this largest rectangular enclosure? \begin{tabular}{|l|l|} \hline□\square□ \\ □\square□ \end{tabular}

Problem 2334

Problem 2335

The function f(x)=3x+5x−1f(x)=3 x+5 x^{-1}f(x)=3x+5x−1 has one local minimum and one local maximum. This function has a local maximum at x=x=x= with value and a local minimum at x=x=x= □\square□ with value □\square□

Problem 2336

Problem 2337

1. Write a third degree polynomial function with integer coefficients that has zeroes x=1x=1x=1 and x=i2x=i \sqrt{2}x=i2​. [You may not leave the function in factored form.]

Problem 2338

Problem 2339

Problem 2340

Problem 2341

Problem 2342

Problem 2343

Problem 2344

The loan amount is a function of time and can be represented by the line of best fit y=15,413−1,635xy=15,413-1,635 xy=15,413−1,635x, where xxx is the number of years. How much is left on the loan after 9 years? (1 point)The loan amount is $\$$ \qquad after 9 years.

Problem 2345

Problem 2346

Question 2 of 10 What are the zeros of this function? A. x=0x=0x=0 and x=−6x=-6x=−6 B. x=0x=0x=0 and x=−9x=-9x=−9 C. x=3x=3x=3 and x=−9x=-9x=−9 D. x=0x=0x=0 and x=6x=6x=6

Problem 2347

Problem 2348

Problem 2349

Problem 2350

Problem 2351

Problem 2352

7. Given f(x)=95x+32f(x)=\frac{9}{5} x+32f(x)=59​x+32, find the following. a. f(60)f(60)f(60) b. f(0)f(0)f(0) c. f(25)f(25)f(25)

Problem 2353

Answer the questions below. \begin{tabular}{|l|l|} \hline (a) Weight loss is affected by the number of calories taken in: the fewer calories taken \\ in, the more weight lost. Which is the dependent variable? \end{tabular}

Problem 2354

Evaluate the expression $\cos ^{-1}\left(\sin \left(\frac{\pi}{3}\right)\right)$ .
Give your answer as an exact value

Find the intervals where the function $f(x) = \frac{1}{2} x^4 - 4x^2 + 7$ is concave upward.

Find the exact value of $\sin \pi$ . $\sin \pi=$

Let $\theta$ be an angle in quadrant I such that $\sin \theta=\frac{7}{10}$ . Find the exact values of $\sec \theta$ and $\tan \theta$ .

The graph of a function $g$ is shown below. Find $g(2)$ and find one value of $x$ for which $g(x)=4$ . (a) $g(2)=$ $\square$ (b) One value of $x$ for which $g(x)=4$ : $\square$

The graph of a function $h$ is shown below. Find one value of $x$ for which $h(x)=1$ and find $h(-2)$ . (a) One value of $x$ for which $h(x)=1$ : $\square$ (b) $h(-2)=$ $\square$

Finding inputs and outputs of a function from its graph
The graph of a function $h$ is shown below. Find $h(-2)$ and find one value of $x$ for which $h(x)=-1$ . (a) $h(-2)=3$ (b) One value of $x$ for which $h(x)=-1$ : $\square$

Find the following derivative: ( 1 Mark) $f(x)=8 x^{3}-\frac{4}{x^{4}} x-12 x-0.1$

340 [EX1] (1) Find the amplitude, period, phase shift, and (2) Graph two periods of each function. (1) $y=2 \sin (2 x+\pi)+2$

Q32) $\lim _{x \rightarrow 1} \frac{\sin (1-\sqrt{x})}{x-1}$ ? a) $-\frac{1}{2}$ b) $1 / 2$

tion de la tangente à la courbe représentative de $f$ au point d'abscisse a. $f(x)=-x^{2}+2 x-8 ; a=-2$

$\lim _{x \rightarrow 2} \frac{x^{3}-2 x^{2}}{x^{2}-5 x+6}$

find $L^{-1}\left\{\frac{s^{2}-40 s-393}{(s-11)\left(s^{2}+4 s+13\right)}\right\}$

5) $f(x)=\frac{x^{3}+x^{2}-2 x}{-3 x^{2}+6 x}$

1. The South Bowie Library and Oxon Hill Library are having a used book sale. The total cost, $y$ , is a function of the number of books, $x$ .
Which function has a greater constant rate of change? Explain. How much cheaper or more expensive is South Bowie Library than Oxon Hill Library? Explain.

Question 3 of 20 This test: 100 point(S) poss This question: 5 point(s) p
Let $F(x)=x^{2}-4$ and $G(x)=3-x$ $(F / G)(x)=$ $\square$ Find $(F / G)(x)$ .

20. State which of the following quadratic functions is in standard form and which is in vertex form. Then find the coordinates of the vertex for each one. A) $s(x)=-(x+5)^{2}-8$ B) $g(x)=-4+3 x-2 x^{2}$

21. You have a 1200 -foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What is the maximum area and the dimensions of this largest rectangular enclosure? \begin{tabular}{|l|l|} \hline $\square$ \\ $\square$ \end{tabular}

The function $f(x)=3 x+5 x^{-1}$ has one local minimum and one local maximum. This function has a local maximum at $x=$ with value and a local minimum at $x=$ $\square$ with value $\square$

1. Write a third degree polynomial function with integer coefficients that has zeroes $x=1$ and $x=i \sqrt{2}$ . [You may not leave the function in factored form.]

The loan amount is a function of time and can be represented by the line of best fit $y=15,413-1,635 x$ , where $x$ is the number of years. How much is left on the loan after 9 years? (1 point)
The loan amount is $\$$ $\qquad$ after 9 years.

Question 2 of 10 What are the zeros of this function? A. $x=0$ and $x=-6$ B. $x=0$ and $x=-9$ C. $x=3$ and $x=-9$ D. $x=0$ and $x=6$

7. Given $f(x)=\frac{9}{5} x+32$ , find the following. a. $f(60)$ b. $f(0)$ c. $f(25)$

If $f(x)=4 x-12$ , what is $f(2) ?$ A. -4 B. 4 C. -20 D. 8

Put the quadratic into vertex form and state the coordinates of the vertex. $y=x^{2}-6 x+21$

10) Let $f(x)=\left(\frac{1}{6}\right)^{x}$ . Find $f(-2)$ . A) $\frac{1}{36}$ B) $-\frac{1}{36}$ C) -12 D) 36

The plot of what function appears below? $f(x)=x^{2}$ $f(x)=-(x-1)^{2}$ $f(x)=-x^{2}+1$ $f(x)=-(x+1)^{2}$ $f(x)=(x-1)^{2}$

Use the table of values of the function $f(x)=-x^{4}+5 x^{3}-7 x+9$ to complete the sentences.
A relative minima is located near $x=5$ A relative maxima is located near Select Choice

Give the equation of the vertical asymptote of the function $f(x)=\log (x-3)$ $\square$ Give domain of the function $f(x)=\log (x-3)$ $\square$ $\square$ Calculator

Factor $f(x)$ into linear factors given that $k$ is a zero of $f(x)$ . 7) $f(x)=x^{3}-48 x-128 ; k=-4$ (multiplicity 2)

Determine the intervals over which the function $d(x) = -x^2 + 2x - 1$ is decreasing.

Use the functions below to find the equation for the indicated operations. $f(x)=x^{2}-2 x-3 \quad g(x)=\frac{x-3}{2 x+3} \quad h(x)=3 x-4$
6. $g(h(x))$