Browse Function problems Studdy Solved!

Problem 5601

The ticket cost for Riverdance is \$40 each.
(a) Define cost function $C(x)$ for $x$ tickets. (b) Write total cost $T(a)$ with 3.5% tax and \ $6 fee. (c) Evaluate$ (T \circ C)(x) $. (d) Find$ (T \circ C)(4)$ and explain its meaning.

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Problem 5602

Find functions $f$ and $g$ where $h(x)=(f \circ g)(x)$ , $f(x) \neq g(x) \neq x$ , and $h(x)=(x+3)^{2}$ .

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Problem 5603

Find the function $(s+t)(x)$ for $s(x)=\frac{x-2}{x^{2}-25}$ and $t(x)=\frac{x-5}{2-x}$ . Write the domain in interval notation.

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Problem 5604

Find $(s \cdot t)(x)$ for $s(x) = \frac{x-3}{x^{2}-36}$ and $t(x) = \frac{x-6}{3-x}$ . State the domain in interval notation.

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Problem 5605

Find the functions for the diameter $d(r)$ and radius $r(d)$ of a sphere given the volume $V(r)=\frac{4}{3} \pi r^{3}$ .

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Problem 5606

The town's population decreases by $8\%$ yearly. If $P(x)=0.92x$ , find $(P \circ P)(x)$ in exact form.

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Problem 5607

Find $(s+t)(x)$ for $s(x)=\frac{x-3}{x^2-36}$ and $t(x)=\frac{x-6}{3-x}$ ; state the domain in interval notation.

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Problem 5608

Find $(f \circ g)(x)$ and its domain in interval notation for $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

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Problem 5609

Evaluate $(f \circ g)(x)$ and find its domain in interval notation, where $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

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Problem 5610

The town's population decreases by $8\%$ yearly. Find $(P \circ P)(x)$ and explain its meaning. Answer in exact form.

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Problem 5611

Find $(f \circ g)(x)$ for $f(x)=\frac{x}{x+9}$ and $g(x)=\frac{8}{x^{2}-1}$ ; state the domain in interval notation.

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Problem 5612

Find the drug amount $D(h)=7 e^{-0.4 h}$ in mg after 5 hours. Options: $5.51$ , $0.3$ , $51.72$ , $0.95$ .

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Problem 5613

Find the domain of $(s \cdot t)(x)=\frac{-1}{x+6}$ , where $s(x)=\frac{x-3}{x^{2}-36}$ and $t(x)=\frac{x-6}{3-x}$ .

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Problem 5614

Find the domain, range, inverse domain, and inverse range of the function $f(x)=\frac{5}{4 x+1}$ .

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Problem 5615

Find the domain, range, inverse domain, and inverse range of the function $f(x)=2x-6$ .

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Problem 5616

How many bacteria are there on day 8 if the population doubles daily with the formula $N(t)=2(2)^{t}$ ?

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Problem 5617

A rabbit population grows at $7\%$ monthly. If there are 260 rabbits now, how many will there be in a year? Use $y=260(2.7)^{0.07 t}$ .

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Problem 5618

Find the domain and range of $f(x)=\sqrt{3+2x}$ and the domain and range of its inverse.

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Problem 5619

Find how many times greater the max speed of a giraffe ( $L=6$ ft) is than a hippo ( $L=3$ ft) using $S=\sqrt{g L}$ with $g=32$ .

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Problem 5620

Find the domain and range of $f(x)=\sqrt{3+2x}$ and its inverse $f^{-1}(x)$ .

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Problem 5621

Find the grams of a radioactive substance after 2 years using $y=6000(2)^{-0.2 t}$ . Round to three decimals.

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Problem 5622

Find the grams of a radioactive substance after 2 years using $y=6000(2)^{-0.2 t}$ . Round to three decimal places.

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Problem 5623

Find the inverse of the one-to-one function $f(x)=\frac{2}{5 x+3}$ .

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Problem 5624

Find the amount of radioactive material after 170 years using $f^{\prime}(x)=700(0.5)^{x / 60}$ . Round to the nearest whole number.

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Problem 5625

Find the inverse of the one-to-one function $f(x)=x^{3}-8$ .

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Problem 5626

Find the inverse of the one-to-one function $f(x)=\frac{6 x+7}{3 x+6}$ .

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Problem 5627

Model the egg production data with a linear function using points (1994, 51.7) and (1998, 60.4). Predict production in 2000.

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Problem 5628

Find the inverse of the one-to-one function $f(x)=x^{2}+4$ for $x \geq 0$ .

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Problem 5629

Find the inverse of the function $f(x)=\frac{9}{5}x+32$ that converts Celsius to Fahrenheit.

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Problem 5630

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, \frac{8}{7}), (0, 1), (1, \frac{7}{8}), (2, \frac{49}{64}), (3, \frac{343}{512})$ .

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Problem 5631

Find the inverse of the one-to-one function $f(x)=\sqrt{x-1}$ .

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Problem 5632

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, 7)$ , $(0, 9)$ , $(1, 11)$ , $(2, 13)$ , $(3, 15)$ .

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Problem 5633

- It will be turned in automatically after the due date. 10. Submit answer Practice similar
Use a change of variables to evaluate the definite integral $\int_{0}^{1}\left(2 x \sqrt{1-x^{2}}\right) d x$ . Leave your final answer as a fraction. $\int_{0}^{1}\left(2 x \sqrt{1-x^{2}}\right) d x=$ $\square$

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Problem 5634

3.7 Implicit Functions
For what point(s) on the curve $x^{2}+y^{2}=2 x$ is the tangent line vertical? $(1,-1)$ and $(0,0)$ $(0,0)$ $(1,1)$ and $(1,-1)$ $(0,0)$ and $(2,0)$

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Problem 5635

This table lists the the yearly profit $P$ (adjusted for inflation) of a certain restaurant, $x$ years after 1970. $P$ is measured thousands of dollars. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $x$ (yrs after 1970 $)$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline $P(1,000$ 's of $\$)$ & 100 & 110 & 100 & 90 & 80 & 105 & 107 \\ \hline \end{tabular}
In what year(s) was the profit $\$ 100000$ ?

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Problem 5636

11. Let a function $y=f(x)$ be given by the equation $y^{3}+y=2 x^{2}$ , and also note that the points $(-1,1)$ , $(0,0)$ and $(1,1)$ lie on its graph. Complete the following table: \begin{tabular}{l|ccc} $x$ & -1 & 0 & 1 \\ \hline $f^{\prime \prime}(x)$ & $A$ & $B$ & $C$ \end{tabular} (a) $A=-1, B=0, C=-1$ (b) $A=-1, B=2, C=-1$ (c) $A=-1, B=4, C=-1$ (d) $A=-\frac{1}{2}, B=4, C=-\frac{1}{2}$ (e) $A=0, B=1, C=0$

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Problem 5637

Name: $\qquad$ Date: $\qquad$
ACMAT161: Calculus I Day 25 Problem Set
A: Practice from Section 5.2: Definite Integrals and 5.3: The Fundamental Theorem of Calculus 1) Create a Riemann sum to estimate the value of $\int_{0}^{2}\left(x^{2}-3\right) d x$ a. Sketch a graph of the integrand on the interval of integration b. Calculate $\Delta x$ and the grid points for $n=$ $\qquad$ $\begin{array}{l} =\frac{b-a}{A}=\frac{2-0}{\Delta}=\frac{x}{\Delta x}=\left(\frac{1}{2}\right)\left\{\begin{array}{l} x_{1}=\left(\frac{1}{2}\right)^{2}-3=-\frac{11}{4} \\ x_{2}=1^{2}-3=-2 \\ x^{3}=\left(\frac{3}{2}\right)^{2}-3=-3 \\ x_{4}=x^{2}-3=1 \end{array}\right. \end{array}$ c. Calculate a $\qquad$ Right Riemann sum 2) Evaluate the following integral using the Fundamental Theorem of Calculus. Discuss whether your result makes sense given the graph of the area. $-\frac{x^{3}}{3}-x^{2}+5 x \quad \int_{0}^{1}\left(x^{2}-2 x+5\right) d x$ $\begin{array}{l} =\frac{1^{3}}{3}-1^{2}+5(1)=\frac{13}{3} \\ =\frac{0^{3}}{3}-D^{2}+5(0)=0 \\ \frac{13}{3}-0=\frac{13}{3} \end{array}$ 3) Find the area of the region bounded by the graph of $f(x)=\sin x$ and the $x$ -axis on the interval $\left[-\frac{3 \pi}{4}, \frac{2 \pi}{3}\right]$ .

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Problem 5638

The velocity function, in feet per second, is given for a particle moving along a straight line $v(t)=t^{2}-t-90,1 \leq t \leq 11$ (a) Find the displacement (in feet). $\square$ ft (b) Find the total distance (in feet) that the particle travels over the given interval.

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Problem 5639

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}-4$ .
Part (b)

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Problem 5640

Use the Midpoint Rule with $n=4$ to approximate the value of the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.) $\int_{3}^{5} \frac{18}{x} d x$

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Problem 5641

Consider the graph shown. a. Select the best possible wording for the situation depicted in the given graph: Ida sells 5 boxes of cookies to family members, and for every door she knocks on in her neighborhood, she sells another 1 boxes of cookies. Ida sells 6 boxes of cookies for every door in her neighborhood that she knocks on. Ida's own family bought 1 boxes of cookies, and for every door in her neighborhood Ida knocks on to sell cookies, she sells 5 additional boxes of cookies. Ida sold \ $1 of cookies to family members, and for every door in her neighborhood she knocks on, she makes another \$5 selling cookies. b. How do we know, based on the given graph, that the relation between the number of doors Ida knocks on, and the number of boxes of cookies she sells, is a linear function? Because the graph is a straight line (or contains points that are arranged in a straight line) and passes the vertical line test. It's impossible to tell from looking at the graph that it represents a linear function. Because on the graph, the$ y-values increase from left to right. Because the graph has units labeled on both axes. c. Fill in the given table with the correct missing values. \begin{tabular}{|c|c|} \hlinex (number of doors Ida knocks on) & y (total number fo boxes of cookies Ida sells) \\ \hline 0 & \square \\ \hline 1 & \square \\ \hline 5 & \\ \hline\square \\ \hline \end{tabular} d. Write the linear function relating the number of doors Ida knocks on, x $, to the total number of boxes of cookies she sells,$ y . y=\square$

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Problem 5642

PREVIOUS ANS
The graph of the second derivative $f$ " of a function $f$ is shown. State the $x$ -coordinates of the inflection points of $f$ . $\square$ $x=8$ (smaller value) $x=3$ (larger value) Need Help? Master it

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Problem 5643

Assignment 4: Problem 11 (1 point)
Find $T_{5}(x)$ , the degree 5 Taylor polynomial of the function $f(x)=\cos (x)$ at $a=0$ . $T_{5}(x)=$ $\square$ Find all values of $x$ for which this approximation is within 0.004794 of the right answer. Assume for simplicity that we limit ourselves to $|x| \leq 1$ . $|x| \leq \square$ $\square$
Note: You can earn partial credit on this problem.

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Problem 5644

find $\int \frac{\ln (x+1)^{2}}{2 x+2} d x$

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Problem 5645

Find the Taylor polynomial of degree 3 for the function $f(x)=\frac{x+7}{x-4}$ about $x=5$ . $T_{3}(x)=\square+\square(x-5)+\square(x-5)^{2}+\square(x-5)^{3}$
Note: You can earn partial credit on this problem.

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Problem 5646

Evaluate the definite integral. $\int_{1}^{8} \frac{1}{x \sqrt{16 x^{2}-3}} d x$

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Problem 5647

Assignment 4: Problem 13 (1 point)
Find the Taylor polynomial with 4 nonzero terms about $x=0$ for the function $f(x)=\int e^{x^{3}} d x, f(0)=0$ .

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Problem 5648

Over the past several years, the owner of a boutique on Aspen Avenue has observed a pattern in the amount of revenue for the store. The revenue reaches a maximum of about $\$ 56000$ in January and a minimum of about $\$ 25000$ in July. Suppose the months are numbered 1 through 12 , and write a function of the form $f(x)=A \sin (B[x-C])+D$ that models the boutique's revenue during the year, where $x$ corresponds to the month. $f(x)=$ $\square$

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Problem 5649

Find the indefinite integral. (Use $C$ for the constant of integration.) $\int \frac{9}{\sqrt{81-(x+9)^{2}}} d x$

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Problem 5650

Determine the interval(s) on which the function is (strictly) increasing. Write your answer as an interval or list of intervals. When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible. Click on "None" if applicable.

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Problem 5651

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $f(x)=x^{2}-2 x-8$

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Problem 5652

Consider the function $f(x)=3 x^{2}-24 x-8$ . a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range.

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Problem 5653

Give the domain and range of the quadratic function whose graph is described. Maximum $=-8$ at $x=9$

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Problem 5654

Question 5 of 10
Write an equation in vertex form of the parabola that has the same shape as the graph of $f(x)=8 x^{2}$ or $g(x)=-8 x^{2}$ , but with the given maximum or minimum. Maximum $=7$ at $x=-5$

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Problem 5655

Consider the function $f(x)=x^{2 / 5}(x-5)$ . This function has two critical numbers $A<B$
Then $A=$ $\square$ and $B$ $\square$ .
For each of the following intervals, tell whether $f(x)$ is increasing or decreasing. $\begin{array}{ll} (-\infty, A]: ? & ? \\ {[A, B]: ?} & \vee \\ {[B, \infty)} & ? \end{array}$
The critical number $A$ is ? $\square$ and the critical number $B$ is $\square$ ? $\square$ There are two numbers $C<D$ where either $f^{\prime \prime}(x)=0$ or $f^{\prime \prime}(x)$ is undefined.
Then $C=$ $\square$ and $D=$ $\square$ Finally for each of the following intervals, tell whether $f(x)$ is concave up or concave down. $(-\infty, C)$ : ? $(C, D)$ ? $\square$ $(D, \infty)$ $?$ $\square$

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Problem 5656

Among all pairs of numbers whose sum is 22 , find a pair whose product is as large as possible. What is the maximum product?

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Problem 5657

In the figure, the coordinates of $P$ are A. $(-3,0)$ . B. $(-4,0)$ . C. $(-5,0)$ . D. $(-6,0)$ . D

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Problem 5658

Erik has 40 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

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Problem 5659

Determine whether the statement makes sense or does not make sense, and explain the reasoning. The student must have made an error when graphing a parabola because its axis of symmetry is the $y$ -axis.

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Problem 5660

The growth of the number of bacteria in a certain population is modeled by a function that increases exponentially over time: Which of the following could describe how the number of bacteria in the population changes each hour? (A) Each hour, the number of bacteria in the population is $16 \%$ greater than it was the previous hour. (B) Each hour, the number of bacteria in the population is 1,600 greater than was the previous hour. (C)
Each hour, the number of bacteria in the population is 1,600 less than it was the previous hour. (D)
Each hour, the number of bacteria in the population is $16 \%$ less than it was the previous hour.

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Problem 5661

The figure shows that when a football is kicked, the nearest defensive player is 6 feet from the point of impact with the kicker's foot. The height of the punted football, $y$ , in feet, can be modeled by the following equation. $y=-0.01 x^{2}+1.18 x+2$
Determine whether the following statement makes sense or does not make sense, and explain your reasoning. The given figure shows that a linear model provides a better description of the football's path than a quadratic model.

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Problem 5662

Jetermine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of $f(x)=-3(x+3)^{2}-6$ has one $y$ -intercept and two $x$ -intercepts.

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Problem 5663

Determine the interval(s). on which the function is constant. Write your answer as an interval or list of intervals. When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible. Click on "None" if applicable. $\square$ $\square$ $\square$ $\square$ $\infty$ None

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Problem 5664

39. Let $p(x)=a x^{3}+b x^{2}+c x+60$ . When $p(x)$ is divided by $x-1$ , the remainder is 30 . When $p(x)$ is divided by $(x-3)(x+7)$ , the quotient is $x-3$ . (a) Find the remainder when $p(x)$ is divided by $(x-3)(x+7)$ .
Explain (b) How many real roots does the equation $p(x)=0$ have? Explain your answer. $\Rightarrow$ Example 14

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Problem 5665

39. Let $p(x)=a x^{3}+b x^{2}+c x+60$ . When $p(x)$ is divided by $x-1$ , the remainder is 30 . When $p(x)$ is divided by $(x-3)(x+7)$ , the quotient is $x-3$ . (a) Find the remainder when $p(x)$ is divided by $(x-3)(x+7)$ . xplain (b) How many real roots does the equation $p(x)=0$ have? Explain your answer. $\Rightarrow$ Example 14

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Problem 5666

The number of bacteria $N$ , in a culture is modeled by the exponential growth model, $N(t)=300 e^{0.025 t}$ , where $t$ represents time in hours. The growth rate of the population of this bacterium is represented by $2.5 \%$ per hour. True False

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Problem 5667

Find the sine, cosine, and tangent of $\angle K$ .
Simplify your answers and write them as proper fractions, improper fractions, or whole numbers. $\begin{array}{l} \sin (K)= \\ \cos (K)= \\ \tan (K)= \end{array}$ $\square$ $\square$ $\square$

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Problem 5668

Determine the exponential rate of increase for the function defined by this table of \begin{tabular}{c|l|} \hline $x$ & $y$ \\ \hline 0 & 4 \\ \hline 1 & 12 \\ \hline 2 & 36 \\ \hline 3 & 108 \\ \hline 4 & 324 \\ \hline \end{tabular}

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Problem 5669

Question Watch Video Show Examples
The derivative of the twice-differentiable function $f$ is shown below on the domain $(-9,9)$ . The graph of $f^{\prime}$ has points of inflection at $x=-3, x=1$ , indicated by small green circles. What inferences can be made about the graphs of $f, f^{\prime}$ , and $f^{\prime \prime}$ on the interval $(-3,0)$ ? Choose the best answer for each dropdown.
Answer Attempt 2 out of 2 From the figure given above, it can be seen that the graph of $f^{\prime}$ on the interval $(-3,0)$ is positive increasing $\square$ , and concave dow $\square$ Based on these observations, it can be concluded that: On the interval $(-3,0)$ , the graph of $f$ would be increasing and concave dow $\vee$ because $f^{\prime}$ is positive and increasing On the interval $(-3,0)$ , the graph of $f^{\prime \prime}$ would be positive only because $f^{\prime}$ is increasing

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Problem 5670

Find the 73th derivative of the function $f(x)=\cos (x)$ .
Answer: $\square$ Preview My Answers Submit Answers

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Problem 5671

Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $(-1,1) \text { and }(5,6)$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The slope is $\square$ (Simplify your answer.) B. The slope is undefined.
Indicate whether the line through the points rises, falls, is horizontal, or is vertical. A. The line is vertical. B. The line falls from left to right. C. The line is horizontal. D. The line rises from left to right.

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Problem 5672

Let $z(x)=\sqrt{\tan (x)}$ . Which of the following best describes its fundamental algebraic structure? composition: A composition $f(g(x))$ of basic functions sum. A sum $f(x)+g(x)$ of basic functions product. A product $f(x) \cdot g(x)$ of basic functions quotient. A quotient $f(x) / g(x)$ of basic functions where $\begin{array}{l} f(x)=\square \\ g(x)=\square \end{array}$

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Problem 5673

Evaluate the following antiderivatives. a) $\int 8 \cos (x)+\sec ^{2}(x) d x=\square+C$

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Problem 5674

To graph the function $g(x) = -f(x+1) + 4$ , use the graph of $y = f(x)$ provided.

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Problem 5675

In the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function. $f(x)=2(x-4)^{2}+3$
The vertex is $\square$ (Type an ordered pair.)

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Problem 5676

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $f(x)=2 x^{2}-20 x+1$
The vertex is $\square$ (Type an ordered pair.)

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Problem 5677

EXAMPLE 2.7.2 Find the derivative of each of the following functions a. $\quad f(x)=\sin ^{-1}(5 x)$ b. $f(x)=\tan ^{-1}(\sqrt{x+1})$ c. $f(t)=t^{2} \sec ^{-1}(2 t)$ d. $f(t)=\sin \left(\cos ^{-1} t\right)$

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Problem 5678

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola's axis of symmetry. Use the parabola to identify the function's domain and range. $f(x)=(x-2)^{2}+4$
Use the graphing tool to graph the equation. Use the vertex and the $y$ -intercept when drawing the graph.
The axis of symmetry is $\square$ (Simplify your answer. Type an equation.) Identify the function's domain. The domain is $\square$ (Type the answer in interval notation.) Identify the function's range. The range is $\square$ (Type the answer in interval notation.)

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Problem 5679

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis graph to determine the domain and range of the function. $f(x)=4 x-x^{2}+12$
Use the graphing tool to graph the equation. Use the vertex and one of the intercepts to draw the graph.
The axis of symmetry is $\square$ (Type an equation.) The domain of the function is $\square$ (Type your answer in interval notation.) The range of the function is $\square$ . (Type your answer in interval notation.)

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Problem 5680

If $f(x)=\int_{0}^{x}\left(36-t^{2}\right) e^{t^{3}} d t$ for all $x$ , then find the largest open interval on which $f$ is increasing.
Answer (in interval notation): $\square$

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Problem 5681

D. negotiate for a higher than market wage hike every year through collective bargaining. b. Suppose that the objective of a union is to maximize the total dues paid to the union by its membership. If union dues are paid as a flat amount per union member employed, the union's strate will be to A. negotiate for the wage level that is consistent with perfectly elastic demand for labor. B. negotiate for the maximum wage rate the employer is willing to pay for the number of workers belonging to the union. C. negotiate for the wage level that is consistent with unit elastic demand for labor. D. negotiate for limiting the entry of new workers over time. Clear all Check answer

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Problem 5682

Graph the logarithmic function. $g(x)=3 \log _{1 / 3} x$
Plot two points on the graph of the function, and also draw the asymptote. Then click on the

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Problem 5683

Draw a line that has the indicated slope and $y$ -intercept. slope $=\frac{3}{2}$ and $y$ -intercept $(0,-5)$
Use the graphing tool on the right to draw the line.
Click to enlarge graph

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Problem 5684

A new television show debuts amid great fanfare, and attracts 14 million viewers for the first episode. The number of viewers for subsequent episodes is shown in the table. \begin{tabular}{|c|c|} \hline Episode \# & \begin{tabular}{c} Viewers \\ (millions) \end{tabular} \\ \hline 1 & 13.9 \\ \hline 2 & 11.1 \\ \hline 3 & 8.8 \\ \hline 4 & 8 \\ \hline 5 & 7.2 \\ \hline 6 & 8.1 \\ \hline 7 & 8.1 \\ \hline 8 & 7.8 \\ \hline 9 & 7.7 \\ \hline \end{tabular}
Use a graphing calculator to find a line of best fit for the data. Round to four decimal places.
Rounding to four decimal places, the line of best fit for the data is $y=$ $\square$ $x+$ $\square$ .

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Problem 5685

Complete the square and find the vertex form of the quadratic function. $\begin{array}{l} f(x)=x^{2}-8 x+59 \\ f(x)=\square \end{array}$

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Problem 5686

If $f(x)=\int_{0}^{x}\left(4-t^{2}\right) e^{t^{2}} d t$ for all $x$ , then find the largest open interval on which $f$ is increasing.
Answer (in interval notation): $\square$

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Problem 5687

If $f(x)=\int_{0}^{x}\left(1-t^{2}\right) e^{t^{3}} d t$ for all $x$ , then find the largest open interval on which $f$ is increasing.
Answer (in interval notation): $\square$

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Problem 5688

Evaluate the integral $\int_{1}^{\sqrt{9}} \frac{1}{1+x^{2}} d x$

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Problem 5689

Suppose $y=3 \sin (4(t+13))-6$ . In your answers, enter pi for $\pi$ . (a) The midline of the graph is the line with equation $y=-6$ help (equations) (b) The amplitude of the graph is 3 help (numbers) (c) The period of the graph is $\pi$ help (numbers)
Note: You can earn partial credit on this problem.

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Problem 5690

1. At what point on the curve $y=e^{2 x}$ is the tangent line parallel to the line $y=2 x$ ? (A) $\left(1, e^{2}\right)$ (B) $(0,1)$ (C) $(0,0)$ (D) $(\ln 2,4)$ (E) $(\ln \sqrt{2}, 2)$

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Problem 5691

Choose the end behavior of the graph of each polynomial function. \begin{tabular}{|l|l|} \hline (a) $f(x)=4 x^{5}-4 x^{4}+4 x^{3}-3 x$ & Falls to the left and rises to the right \\ Rises to the left and falls to the right \\ Rises to the left and rises to the right \\ (b) $f(x)=5 x^{4}-3 x^{3}-2 x^{2}-6$ & Falls to the left and falls to the right and rises to the right \\ Rises to the left and falls to the right \\ (c) $f(x)=-4(x-3)^{2}(x+2)^{2}$ & Falls to the left and falls to the right and rises to the right \\ Rises to the left and falls to the right \\ Rises to the left and rises to the right rises to the right \\ Falls to the left and falls to the right \\ \hline \end{tabular}

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Problem 5692

Graph all vertical and horizontal asymptotes of the rational function. $f(x)=\frac{x+1}{-x^{2}-6}$

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Problem 5693

3.12 An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of $T$ , the number of years to maturity for a randomly selected bond, is $F(t)=\left\{\begin{array}{ll} 0, & t<1, \\ \frac{1}{4}, & 1 \leq t<3, \\ \frac{1}{2}, & 3 \leq t<5, \\ \frac{3}{4}, & 5 \leq t<7, \\ 1, & t \geq 7, \end{array}\right.$ find (a) $P(T=5)$ ;

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Problem 5694

Example (2) (Activity)
The range of the function $y=4 \sin 2 \theta$ is $\qquad$ (3) $[-4,4]$ (b) $\{-4,4\}$ (C) $[-2,2]$ (d) $]-2,2$ [ Sol.

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Problem 5695

Submit Answer 11. [-/1 Points] DETAILS MY NOTES SCALCET9M 4.4.015.
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. $\lim _{t \rightarrow 0} \frac{e^{8 t}-1}{\sin (t)}$ $\square$ Need Help? Read It Watch It Submit Answer
12. [-/1 Points] DETAILS

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Problem 5696

15. [-/1 Points] DETAILS MY NOTES SCALCET9M 4.4.031.
Find the limit. Use I'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. $\lim _{x \rightarrow 0} \frac{\sin ^{-1}(x)}{2 x}$ $\square$ Need Help? Read It Watch it Submit Answer

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Problem 5697

18. [-/1 Points]
DETAILS MY NOTES
SCALCET9M 4.4.058. ASK YOL
Find the limit. Use I'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. $\lim _{x \rightarrow 0^{+}}(\tan (8 x))^{x}$ $\square$ Need Help? Read It

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Problem 5698

Q.12 A long term investment of $\$ 500,000$ has been made by a small company. If all interest is reinvested at the same rate of interest. Required: a) What will the future value of the investment be after 10 years? The interest rate is $9 \%$ per year compounded quarterly. b) What will the profit value of the investment be after 10 years? The interest rate is $9 \%$ per year compounded quarterly. c) What will future value and net profit of the investment be after $18^{\text {ret }}$ quarters? The interest rate is $12 \%$ per year compounded quarterly. d) What will future value and net profit of the investment be after $7^{\text {th }}$ semi-annual, if the investment rate be $8 \%$ per year compounded semi-annually? e) What will future value and net profit of the investment be after $42^{\text {nd }}$ months, if the investment rate be $9 \%$ per year compounded monthly? Ise single-payment formula to compute desire results.

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Problem 5699

2. Compute the derivative $D_{f}$ for each of the following functio (a) $f(t)=\begin{array}{c}t^{2} \\ t \cos (t)\end{array}$ (b) $f(x, y)=x^{2} y^{3} \cos (x y)$ (c) $f(x, y)=\left[\begin{array}{c}x+y \\ x y \\ x^{2} e^{y}\end{array}\right]$

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Problem 5700

11. Geben Sie die in kartesischer Binomialform gegebenen Punkte in Polarform an $A(-6 /-8), B=\left[8 ; 120^{\circ}\right], C(-5 / 3), D(5 / 0), E=\left[\sqrt{ } 12 ; 4,2^{\mathrm{rad}}\right], F=[5 ; \pi / 2]$
12. Skizzieren Sie am Einheitskreis die folgenden Funktionswerte. a. $\sin \left(250^{\circ}\right)$ b. $\cos \left(40^{\circ}\right)$ c. $\sin \left(\pi / 3^{\text {rad }}\right)$ d. $\cos \left(5^{\text {rad }}\right)$ e. $\sin \left(-70^{\circ}\right)$

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Function

Problem 5601

The ticket cost for Riverdance is \$40 each. (a) Define cost function C(x)C(x)C(x) for xxx tickets. (b) Write total cost T(a)T(a)T(a) with 3.5% tax and \6fee.(c)Evaluate6 fee. (c) Evaluate 6fee.(c)Evaluate(T \circ C)(x).(d)Find. (d) Find .(d)Find(T \circ C)(4)$ and explain its meaning.

Problem 5602

Find functions fff and ggg where h(x)=(f∘g)(x)h(x)=(f \circ g)(x)h(x)=(f∘g)(x), f(x)≠g(x)≠xf(x) \neq g(x) \neq xf(x)=g(x)=x, and h(x)=(x+3)2h(x)=(x+3)^{2}h(x)=(x+3)2.

Problem 5603

Find the function (s+t)(x)(s+t)(x)(s+t)(x) for s(x)=x−2x2−25s(x)=\frac{x-2}{x^{2}-25}s(x)=x2−25x−2​ and t(x)=x−52−xt(x)=\frac{x-5}{2-x}t(x)=2−xx−5​. Write the domain in interval notation.

Problem 5604

Find (s⋅t)(x)(s \cdot t)(x)(s⋅t)(x) for s(x)=x−3x2−36s(x) = \frac{x-3}{x^{2}-36}s(x)=x2−36x−3​ and t(x)=x−63−xt(x) = \frac{x-6}{3-x}t(x)=3−xx−6​. State the domain in interval notation.

Problem 5605

Find the functions for the diameter d(r)d(r)d(r) and radius r(d)r(d)r(d) of a sphere given the volume V(r)=43πr3V(r)=\frac{4}{3} \pi r^{3}V(r)=34​πr3.

Problem 5606

The town's population decreases by 8%8\%8% yearly. If P(x)=0.92xP(x)=0.92xP(x)=0.92x, find (P∘P)(x)(P \circ P)(x)(P∘P)(x) in exact form.

Problem 5607

Find (s+t)(x)(s+t)(x)(s+t)(x) for s(x)=x−3x2−36s(x)=\frac{x-3}{x^2-36}s(x)=x2−36x−3​ and t(x)=x−63−xt(x)=\frac{x-6}{3-x}t(x)=3−xx−6​; state the domain in interval notation.

Problem 5608

Find (f∘g)(x)(f \circ g)(x)(f∘g)(x) and its domain in interval notation for f(x)=xx−1f(x)=\frac{x}{x-1}f(x)=x−1x​ and g(x)=13x2−36g(x)=\frac{13}{x^{2}-36}g(x)=x2−3613​.

Problem 5609

Evaluate (f∘g)(x)(f \circ g)(x)(f∘g)(x) and find its domain in interval notation, where f(x)=xx−1f(x)=\frac{x}{x-1}f(x)=x−1x​ and g(x)=13x2−36g(x)=\frac{13}{x^{2}-36}g(x)=x2−3613​.

Problem 5610

The town's population decreases by 8%8\%8% yearly. Find (P∘P)(x)(P \circ P)(x)(P∘P)(x) and explain its meaning. Answer in exact form.

Problem 5611

Find (f∘g)(x)(f \circ g)(x)(f∘g)(x) for f(x)=xx+9f(x)=\frac{x}{x+9}f(x)=x+9x​ and g(x)=8x2−1g(x)=\frac{8}{x^{2}-1}g(x)=x2−18​; state the domain in interval notation.

Problem 5612

Find the drug amount D(h)=7e−0.4hD(h)=7 e^{-0.4 h}D(h)=7e−0.4h in mg after 5 hours. Options: 5.515.515.51, 0.30.30.3, 51.7251.7251.72, 0.950.950.95.

Problem 5613

Find the domain of (s⋅t)(x)=−1x+6(s \cdot t)(x)=\frac{-1}{x+6}(s⋅t)(x)=x+6−1​, where s(x)=x−3x2−36s(x)=\frac{x-3}{x^{2}-36}s(x)=x2−36x−3​ and t(x)=x−63−xt(x)=\frac{x-6}{3-x}t(x)=3−xx−6​.

Problem 5614

Find the domain, range, inverse domain, and inverse range of the function f(x)=54x+1f(x)=\frac{5}{4 x+1}f(x)=4x+15​.

Problem 5615

Find the domain, range, inverse domain, and inverse range of the function f(x)=2x−6f(x)=2x-6f(x)=2x−6.

Problem 5616

How many bacteria are there on day 8 if the population doubles daily with the formula N(t)=2(2)tN(t)=2(2)^{t}N(t)=2(2)t?

Problem 5617

A rabbit population grows at 7%7\%7% monthly. If there are 260 rabbits now, how many will there be in a year? Use y=260(2.7)0.07ty=260(2.7)^{0.07 t}y=260(2.7)0.07t.

Problem 5618

Find the domain and range of f(x)=3+2xf(x)=\sqrt{3+2x}f(x)=3+2x​ and the domain and range of its inverse.

Problem 5619

Find how many times greater the max speed of a giraffe (L=6L=6L=6 ft) is than a hippo (L=3L=3L=3 ft) using S=gLS=\sqrt{g L}S=gL​ with g=32g=32g=32.

Problem 5620

Find the domain and range of f(x)=3+2xf(x)=\sqrt{3+2x}f(x)=3+2x​ and its inverse f−1(x)f^{-1}(x)f−1(x).

Problem 5621

Find the grams of a radioactive substance after 2 years using y=6000(2)−0.2ty=6000(2)^{-0.2 t}y=6000(2)−0.2t. Round to three decimals.

Problem 5622

Find the grams of a radioactive substance after 2 years using y=6000(2)−0.2ty=6000(2)^{-0.2 t}y=6000(2)−0.2t. Round to three decimal places.

Problem 5623

Find the inverse of the one-to-one function f(x)=25x+3f(x)=\frac{2}{5 x+3}f(x)=5x+32​.

Problem 5624

Find the amount of radioactive material after 170 years using f′(x)=700(0.5)x/60f^{\prime}(x)=700(0.5)^{x / 60}f′(x)=700(0.5)x/60. Round to the nearest whole number.

Problem 5625

Find the inverse of the one-to-one function f(x)=x3−8f(x)=x^{3}-8f(x)=x3−8.

Problem 5626

Find the inverse of the one-to-one function f(x)=6x+73x+6f(x)=\frac{6 x+7}{3 x+6}f(x)=3x+66x+7​.

Problem 5627

Model the egg production data with a linear function using points (1994, 51.7) and (1998, 60.4). Predict production in 2000.

Problem 5628

Find the inverse of the one-to-one function f(x)=x2+4f(x)=x^{2}+4f(x)=x2+4 for x≥0x \geq 0x≥0.

Problem 5629

Find the inverse of the function f(x)=95x+32f(x)=\frac{9}{5}x+32f(x)=59​x+32 that converts Celsius to Fahrenheit.

Problem 5630

Is the function H(x)H(x)H(x) exponential? If yes, find the base aaa. Given points: (−1,87),(0,1),(1,78),(2,4964),(3,343512)(-1, \frac{8}{7}), (0, 1), (1, \frac{7}{8}), (2, \frac{49}{64}), (3, \frac{343}{512})(−1,78​),(0,1),(1,87​),(2,6449​),(3,512343​).

Problem 5631

Find the inverse of the one-to-one function f(x)=x−1f(x)=\sqrt{x-1}f(x)=x−1​.

Problem 5632

Is the function H(x)H(x)H(x) exponential? If yes, find the base aaa. Given points: (−1,7)(-1, 7)(−1,7), (0,9)(0, 9)(0,9), (1,11)(1, 11)(1,11), (2,13)(2, 13)(2,13), (3,15)(3, 15)(3,15).

Problem 5633

Problem 5634

3.7 Implicit FunctionsFor what point(s) on the curve x2+y2=2xx^{2}+y^{2}=2 xx2+y2=2x is the tangent line vertical? (1,−1)(1,-1)(1,−1) and (0,0)(0,0)(0,0) (0,0)(0,0)(0,0) (1,1)(1,1)(1,1) and (1,−1)(1,-1)(1,−1) (0,0)(0,0)(0,0) and (2,0)(2,0)(2,0)

Problem 5635

Problem 5636

Problem 5637

Problem 5638

Problem 5639

Translate each graph as specified below. (a) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=(x+5)2y=(x+5)^{2}y=(x+5)2. (b) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=x2−4y=x^{2}-4y=x2−4.Part (b)

Problem 5640

Use the Midpoint Rule with n=4n=4n=4 to approximate the value of the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.) ∫3518xdx\int_{3}^{5} \frac{18}{x} d x∫35​x18​dx

Problem 5641

Problem 5642

PREVIOUS ANSThe graph of the second derivative fff " of a function fff is shown. State the xxx-coordinates of the inflection points of fff. □\square□ x=8x=8x=8 (smaller value) x=3x=3x=3 (larger value) Need Help? Master it

Problem 5643

The ticket cost for Riverdance is \$40 each.
(a) Define cost function $C(x)$ for $x$ tickets. (b) Write total cost $T(a)$ with 3.5% tax and \ $6 fee. (c) Evaluate$ (T \circ C)(x) $. (d) Find$ (T \circ C)(4)$ and explain its meaning.

Find functions $f$ and $g$ where $h(x)=(f \circ g)(x)$ , $f(x) \neq g(x) \neq x$ , and $h(x)=(x+3)^{2}$ .

Find the function $(s+t)(x)$ for $s(x)=\frac{x-2}{x^{2}-25}$ and $t(x)=\frac{x-5}{2-x}$ . Write the domain in interval notation.

Find $(s \cdot t)(x)$ for $s(x) = \frac{x-3}{x^{2}-36}$ and $t(x) = \frac{x-6}{3-x}$ . State the domain in interval notation.

Find the functions for the diameter $d(r)$ and radius $r(d)$ of a sphere given the volume $V(r)=\frac{4}{3} \pi r^{3}$ .

The town's population decreases by $8\%$ yearly. If $P(x)=0.92x$ , find $(P \circ P)(x)$ in exact form.

Find $(s+t)(x)$ for $s(x)=\frac{x-3}{x^2-36}$ and $t(x)=\frac{x-6}{3-x}$ ; state the domain in interval notation.

Find $(f \circ g)(x)$ and its domain in interval notation for $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

Evaluate $(f \circ g)(x)$ and find its domain in interval notation, where $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

The town's population decreases by $8\%$ yearly. Find $(P \circ P)(x)$ and explain its meaning. Answer in exact form.

Find $(f \circ g)(x)$ for $f(x)=\frac{x}{x+9}$ and $g(x)=\frac{8}{x^{2}-1}$ ; state the domain in interval notation.

Find the drug amount $D(h)=7 e^{-0.4 h}$ in mg after 5 hours. Options: $5.51$ , $0.3$ , $51.72$ , $0.95$ .

Find the domain of $(s \cdot t)(x)=\frac{-1}{x+6}$ , where $s(x)=\frac{x-3}{x^{2}-36}$ and $t(x)=\frac{x-6}{3-x}$ .

Find the domain, range, inverse domain, and inverse range of the function $f(x)=\frac{5}{4 x+1}$ .

Find the domain, range, inverse domain, and inverse range of the function $f(x)=2x-6$ .

How many bacteria are there on day 8 if the population doubles daily with the formula $N(t)=2(2)^{t}$ ?

A rabbit population grows at $7\%$ monthly. If there are 260 rabbits now, how many will there be in a year? Use $y=260(2.7)^{0.07 t}$ .

Find the domain and range of $f(x)=\sqrt{3+2x}$ and the domain and range of its inverse.

Find how many times greater the max speed of a giraffe ( $L=6$ ft) is than a hippo ( $L=3$ ft) using $S=\sqrt{g L}$ with $g=32$ .

Find the domain and range of $f(x)=\sqrt{3+2x}$ and its inverse $f^{-1}(x)$ .

Find the grams of a radioactive substance after 2 years using $y=6000(2)^{-0.2 t}$ . Round to three decimals.

Find the grams of a radioactive substance after 2 years using $y=6000(2)^{-0.2 t}$ . Round to three decimal places.

Find the inverse of the one-to-one function $f(x)=\frac{2}{5 x+3}$ .

Find the amount of radioactive material after 170 years using $f^{\prime}(x)=700(0.5)^{x / 60}$ . Round to the nearest whole number.

Find the inverse of the one-to-one function $f(x)=x^{3}-8$ .

Find the inverse of the one-to-one function $f(x)=\frac{6 x+7}{3 x+6}$ .

Find the inverse of the one-to-one function $f(x)=x^{2}+4$ for $x \geq 0$ .

Find the inverse of the function $f(x)=\frac{9}{5}x+32$ that converts Celsius to Fahrenheit.

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, \frac{8}{7}), (0, 1), (1, \frac{7}{8}), (2, \frac{49}{64}), (3, \frac{343}{512})$ .

Find the inverse of the one-to-one function $f(x)=\sqrt{x-1}$ .

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, 7)$ , $(0, 9)$ , $(1, 11)$ , $(2, 13)$ , $(3, 15)$ .

3.7 Implicit Functions
For what point(s) on the curve $x^{2}+y^{2}=2 x$ is the tangent line vertical? $(1,-1)$ and $(0,0)$ $(0,0)$ $(1,1)$ and $(1,-1)$ $(0,0)$ and $(2,0)$

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}-4$ .
Part (b)

Use the Midpoint Rule with $n=4$ to approximate the value of the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.) $\int_{3}^{5} \frac{18}{x} d x$

PREVIOUS ANS
The graph of the second derivative $f$ " of a function $f$ is shown. State the $x$ -coordinates of the inflection points of $f$ . $\square$ $x=8$ (smaller value) $x=3$ (larger value) Need Help? Master it

find $\int \frac{\ln (x+1)^{2}}{2 x+2} d x$

Evaluate the definite integral. $\int_{1}^{8} \frac{1}{x \sqrt{16 x^{2}-3}} d x$

Assignment 4: Problem 13 (1 point)
Find the Taylor polynomial with 4 nonzero terms about $x=0$ for the function $f(x)=\int e^{x^{3}} d x, f(0)=0$ .

Find the indefinite integral. (Use $C$ for the constant of integration.) $\int \frac{9}{\sqrt{81-(x+9)^{2}}} d x$

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $f(x)=x^{2}-2 x-8$

Consider the function $f(x)=3 x^{2}-24 x-8$ . a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range.

Give the domain and range of the quadratic function whose graph is described. Maximum $=-8$ at $x=9$

Question 5 of 10
Write an equation in vertex form of the parabola that has the same shape as the graph of $f(x)=8 x^{2}$ or $g(x)=-8 x^{2}$ , but with the given maximum or minimum. Maximum $=7$ at $x=-5$

In the figure, the coordinates of $P$ are A. $(-3,0)$ . B. $(-4,0)$ . C. $(-5,0)$ . D. $(-6,0)$ . D

Determine whether the statement makes sense or does not make sense, and explain the reasoning. The student must have made an error when graphing a parabola because its axis of symmetry is the $y$ -axis.

Jetermine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of $f(x)=-3(x+3)^{2}-6$ has one $y$ -intercept and two $x$ -intercepts.

The number of bacteria $N$ , in a culture is modeled by the exponential growth model, $N(t)=300 e^{0.025 t}$ , where $t$ represents time in hours. The growth rate of the population of this bacterium is represented by $2.5 \%$ per hour. True False

Determine the exponential rate of increase for the function defined by this table of \begin{tabular}{c|l|} \hline $x$ & $y$ \\ \hline 0 & 4 \\ \hline 1 & 12 \\ \hline 2 & 36 \\ \hline 3 & 108 \\ \hline 4 & 324 \\ \hline \end{tabular}

Find the 73th derivative of the function $f(x)=\cos (x)$ .
Answer: $\square$ Preview My Answers Submit Answers

Evaluate the following antiderivatives. a) $\int 8 \cos (x)+\sec ^{2}(x) d x=\square+C$

To graph the function $g(x) = -f(x+1) + 4$ , use the graph of $y = f(x)$ provided.