Question 1

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. A 16-month old baby named Amelia weighs $w(19)$ pounds. What does this tell you?

Accepted Answer

A)  She is below average weight. 
B)  She is above average weight. 
C)  She is about average weight. 
A)  She is below average weight. 
B)  She is above average weight. 
C)  She is about average weight.

Question 2

Let $f$ and $g$ be two invertible functions such that $f^{-1}(x)=(x-2)^{3}$ and $g(x)=2 x+2$. Find $f\left(g^{-1}(4)\right)$. Round your answer to two decimal places, if necessary.

Accepted Answer

The answer of Let $f$ and $g$ be two invertible...

Question 3

What are the units of $f^{-1}(H)$ if $H=f(t)$ is the average height, in inches, of a plant $t$ weeks old?

Accepted Answer

The answer of What are the units of $f^{-1}(H)$ if...

Question 4

Use the following chart containing values of $f(x)$ to determine whether the function appears to be:
a) increasing or decreasing
b) concave up or concave down

Accepted Answer

a) increas

Question 5

Let $f$ and $g$ be two invertible functions such that $f^{-1}(x)=(x-5)^{3}$ and $g(x)=5 x+2$. Find $f(g(4))$. Round your answer to two decimal places, if necessary.

Accepted Answer

The answer of Let $f$ and $g$ be two invertible...

Question 6

Find the domain of the function $h(x)=\frac{2}{x^{2}-25}$.

Accepted Answer

All real n

Question 7

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \ 3 x+4, & x>0\end{cases}$
Graph the function.

Accepted Answer

The answer of Let \(f(x)= \begin{cases}2 x-5, & x \leq...

Question 8

The circumference, in $\mathrm{cm}$, of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$. If $C=f(r)$, evaluate and interpret $f^{-1}(14 \pi)$.

Accepted Answer

A)  $28 \pi^{2}$, the circumference of a circle with radius $14 \pi$. 
B)  $28 \pi^{2}$, the radius of a circle with circumference $14 \pi$. 
C)  7 , the circumference of a circle with radius $14 \pi$. 
D)  7 , the radius of a circle with circumference $14 \pi$. 
A)  $28 \pi^{2}$, the circumference of a circle with radius $14 \pi$. 
B)  $28 \pi^{2}$, the radius of a circle with circumference $14 \pi$. 
C)  7 , the circumference of a circle with radius $14 \pi$. 
D)  7 , the radius of a circle with circumference $14 \pi$.

Question 9

The pollution decreased more slowly as time went on. Which of the following statements describes the graph of quantity of pollution against time?

Accepted Answer

A)  Increasing and concave up 
B)  Decreasing and concave up 
C)  Increasing and concave down 
D)  Decreasing and concave down 
E)  None of the above 
A)  Increasing and concave up 
B)  Decreasing and concave up 
C)  Increasing and concave down 
D)  Decreasing and concave down 
E)  None of the above

Question 10

Let $f(x)=2 x^{2}-5$. For what value of $x$ is $f(x)=27$ ?

Accepted Answer

The answer of Let $f(x)=2 x^{2}-5$. For what value of...

Question 11

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.35$ for each minute (or part of a minute) over 100 minutes.
a) Write a formula for the company's policy.
b) How much is Fred's cell phone bill for the month if he talks for 138 minutes.

Accepted Answer

The answer of Fred's cell phone company charges $\$ 60$...

Question 12

What is the range of the function $y=\frac{14}{\sqrt{4-x^{2}}}$ ?

Accepted Answer

A)  $y \geq 2$ 
B)  $y \leq 2$ 
C)  $y \geq 14$ 
D)  $y \leq 14$ 
E)  $y \geq 7$
F) $y \leq 7$ 
A)  $y \geq 2$ 
B)  $y \leq 2$ 
C)  $y \geq 14$ 
D)  $y \leq 14$ 
E)  $y \geq 7$
F) $y \leq 7$

Question 13

Given $f(x)=4 x^{2}-2$ and $g(x)=-3 x+1$, find $f(g(5))$ and $g(f(5))$.

Accepted Answer

The answer of Given $f(x)=4 x^{2}-2$ and $g(x)=-3 x+1$, find...

Question 14

Use the definition of absolute value to write a piecewise formula for $f(x)=\left|3 x^{2}-27\right|$.

Accepted Answer

The answer of Use the definition of absolute value to...

Question 15

Find the $y$-coordinate of the point on the graph of $y=h(x)=\frac{1}{\sqrt{x+3}}$ whose $x$-coordinate is 1 .

Accepted Answer

The answer of Find the $y$-coordinate of the point on...

Question 16

Let $C(f(t))$ be a composite function, where $V=f(t)$ is the volume of water, in cubic feet, emitted by a sprinkler system after $t$ minutes, and $C(V)$ is the cost, in dollars, of $V$ cubic feet of water. What are the units of $C(f(t))$ ?

Accepted Answer

A)  cubic feet 
B)  minutes 
C)  dollars 
A)  cubic feet 
B)  minutes 
C)  dollars

Question 17

Sketch the graph of $f(x)=(x-4)^{2}+2$

Accepted Answer

The answer of Sketch the graph of $f(x)=(x-4)^{2}+2$...

Question 18

Let $f(x)=\frac{6}{\sqrt{x+21}}$ and $g(x)=x^{2}-10 x$. Is $x=6$ in the domain of $f(g(x))$ ?

Accepted Answer

A) True 
 B)False

Question 19

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.45$ for each minute (or part of a minute) over 105 minutes. Which of the following is the domain of the function?

Accepted Answer

A)  $ x \geq 0$ 
B)  $ x \geq 60$ 
C)  $x \geq 105$ 
D)  $0 \leq x \leq 105$ 
A)  $ x \geq 0$ 
B)  $ x \geq 60$ 
C)  $x \geq 105$ 
D)  $0 \leq x \leq 105$

Question 20

A model rocket is launched from the roof of a building. For height $h$, in meters, and time $t$, in seconds, after the rocket is launched, the height of the rocket above the ground is given by $h=f(t)=-4.9 t^{2}+43 t+21$. Interpret the domain of the graph of $f(t)$.

Accepted Answer

A)  The time it takes for the rocket to hit the ground 
B)  The rocket's initial height 
C)  The heights the rocket reaches 
D)  The time the rocket is in the air 
E)  The maximum height obtained by the rocket. 
A)  The time it takes for the rocket to hit the ground 
B)  The rocket's initial height 
C)  The heights the rocket reaches 
D)  The time the rocket is in the air 
E)  The maximum height obtained by the rocket.

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. A 16-month old baby named Amelia weighs $w(19)$ pounds. What does this tell you?

Let $f$ and $g$ be two invertible functions such that $f^{-1}(x)=(x-2)^{3}$ and $g(x)=2 x+2$ . Find $f\left(g^{-1}(4)\right)$ . Round your answer to two decimal places, if necessary.

What are the units of $f^{-1}(H)$ if $H=f(t)$ is the average height, in inches, of a plant $t$ weeks old?

Use the following chart containing values of $f(x)$ to determine whether the function appears to be: a) increasing or decreasing b) concave up or concave down

Let $f$ and $g$ be two invertible functions such that $f^{-1}(x)=(x-5)^{3}$ and $g(x)=5 x+2$ . Find $f(g(4))$ . Round your answer to two decimal places, if necessary.

Find the domain of the function $h(x)=\frac{2}{x^{2}-25}$ .

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+4, & x>0\end{cases}$ Graph the function.

The circumference, in $\mathrm{cm}$ , of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$ . If $C=f(r)$ , evaluate and interpret $f^{-1}(14 \pi)$ .

The pollution decreased more slowly as time went on. Which of the following statements describes the graph of quantity of pollution against time?

Let $f(x)=2 x^{2}-5$ . For what value of $x$ is $f(x)=27$ ?

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.35$ for each minute (or part of a minute) over 100 minutes. a) Write a formula for the company's policy. b) How much is Fred's cell phone bill for the month if he talks for 138 minutes.

What is the range of the function $y=\frac{14}{\sqrt{4-x^{2}}}$ ?

Given $f(x)=4 x^{2}-2$ and $g(x)=-3 x+1$ , find $f(g(5))$ and $g(f(5))$ .

Use the definition of absolute value to write a piecewise formula for $f(x)=\left|3 x^{2}-27\right|$ .

Find the $y$ -coordinate of the point on the graph of $y=h(x)=\frac{1}{\sqrt{x+3}}$ whose $x$ -coordinate is 1 .

Let $C(f(t))$ be a composite function, where $V=f(t)$ is the volume of water, in cubic feet, emitted by a sprinkler system after $t$ minutes, and $C(V)$ is the cost, in dollars, of $V$ cubic feet of water. What are the units of $C(f(t))$ ?

Sketch the graph of $f(x)=(x-4)^{2}+2$

Let $f(x)=\frac{6}{\sqrt{x+21}}$ and $g(x)=x^{2}-10 x$ . Is $x=6$ in the domain of $f(g(x))$ ?

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.45$ for each minute (or part of a minute) over 105 minutes. Which of the following is the domain of the function?

A model rocket is launched from the roof of a building. For height $h$ , in meters, and time $t$ , in seconds, after the rocket is launched, the height of the rocket above the ground is given by $h=f(t)=-4.9 t^{2}+43 t+21$ . Interpret the domain of the graph of $f(t)$ .

Linear Functions and Change

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Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

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Exam 2: Functions

Let w(m)w(m)w(m) give the weight (in pounds) of an average-sized baby girl who is mmm months old. A 16-month old baby named Amelia weighs w(19)w(19)w(19) pounds. What does this tell you?

Let fff and ggg be two invertible functions such that f−1(x)=(x−2)3f^{-1}(x)=(x-2)^{3}f−1(x)=(x−2)3 and g(x)=2x+2g(x)=2 x+2g(x)=2x+2 . Find f(g−1(4))f\left(g^{-1}(4)\right)f(g−1(4)) . Round your answer to two decimal places, if necessary.

What are the units of f−1(H)f^{-1}(H)f−1(H) if H=f(t)H=f(t)H=f(t) is the average height, in inches, of a plant ttt weeks old?

Use the following chart containing values of f(x)f(x)f(x) to determine whether the function appears to be: a) increasing or decreasing b) concave up or concave down

Let fff and ggg be two invertible functions such that f−1(x)=(x−5)3f^{-1}(x)=(x-5)^{3}f−1(x)=(x−5)3 and g(x)=5x+2g(x)=5 x+2g(x)=5x+2 . Find f(g(4))f(g(4))f(g(4)) . Round your answer to two decimal places, if necessary.

Find the domain of the function h(x)=2x2−25h(x)=\frac{2}{x^{2}-25}h(x)=x2−252​ .

Let f(x)={2x−5,x≤03x+4,x>0f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+4, & x>0\end{cases}f(x)={2x−5,3x+4,​x≤0x>0​ Graph the function.

The circumference, in cm\mathrm{cm}cm , of a circle whose radius is r cmr \mathrm{~cm}r cm is given by C=2πrC=2 \pi rC=2πr . If C=f(r)C=f(r)C=f(r) , evaluate and interpret f−1(14π)f^{-1}(14 \pi)f−1(14π) .

The pollution decreased more slowly as time went on. Which of the following statements describes the graph of quantity of pollution against time?

Let f(x)=2x2−5f(x)=2 x^{2}-5f(x)=2x2−5 . For what value of xxx is f(x)=27f(x)=27f(x)=27 ?

Fred's cell phone company charges $60\$ 60$60 per month and $0.35\$ 0.35$0.35 for each minute (or part of a minute) over 100 minutes. a) Write a formula for the company's policy. b) How much is Fred's cell phone bill for the month if he talks for 138 minutes.

What is the range of the function y=144−x2y=\frac{14}{\sqrt{4-x^{2}}}y=4−x2​14​ ?

Given f(x)=4x2−2f(x)=4 x^{2}-2f(x)=4x2−2 and g(x)=−3x+1g(x)=-3 x+1g(x)=−3x+1 , find f(g(5))f(g(5))f(g(5)) and g(f(5))g(f(5))g(f(5)) .

Use the definition of absolute value to write a piecewise formula for f(x)=∣3x2−27∣f(x)=\left|3 x^{2}-27\right|f(x)=​3x2−27​ .

Find the yyy -coordinate of the point on the graph of y=h(x)=1x+3y=h(x)=\frac{1}{\sqrt{x+3}}y=h(x)=x+3​1​ whose xxx -coordinate is 1 .

Let C(f(t))C(f(t))C(f(t)) be a composite function, where V=f(t)V=f(t)V=f(t) is the volume of water, in cubic feet, emitted by a sprinkler system after ttt minutes, and C(V)C(V)C(V) is the cost, in dollars, of VVV cubic feet of water. What are the units of C(f(t))C(f(t))C(f(t)) ?

Sketch the graph of f(x)=(x−4)2+2f(x)=(x-4)^{2}+2f(x)=(x−4)2+2

Let f(x)=6x+21f(x)=\frac{6}{\sqrt{x+21}}f(x)=x+21​6​ and g(x)=x2−10xg(x)=x^{2}-10 xg(x)=x2−10x . Is x=6x=6x=6 in the domain of f(g(x))f(g(x))f(g(x)) ?

Fred's cell phone company charges $60\$ 60$60 per month and $0.45\$ 0.45$0.45 for each minute (or part of a minute) over 105 minutes. Which of the following is the domain of the function?

Linear Functions and Change

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

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Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. A 16-month old baby named Amelia weighs $w(19)$ pounds. What does this tell you?

Let $f$ and $g$ be two invertible functions such that $f^{-1}(x)=(x-2)^{3}$ and $g(x)=2 x+2$ . Find $f\left(g^{-1}(4)\right)$ . Round your answer to two decimal places, if necessary.

What are the units of $f^{-1}(H)$ if $H=f(t)$ is the average height, in inches, of a plant $t$ weeks old?

Use the following chart containing values of $f(x)$ to determine whether the function appears to be: a) increasing or decreasing b) concave up or concave down

Let $f$ and $g$ be two invertible functions such that $f^{-1}(x)=(x-5)^{3}$ and $g(x)=5 x+2$ . Find $f(g(4))$ . Round your answer to two decimal places, if necessary.

Find the domain of the function $h(x)=\frac{2}{x^{2}-25}$ .

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+4, & x>0\end{cases}$ Graph the function.

The circumference, in $\mathrm{cm}$ , of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$ . If $C=f(r)$ , evaluate and interpret $f^{-1}(14 \pi)$ .

Let $f(x)=2 x^{2}-5$ . For what value of $x$ is $f(x)=27$ ?

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.35$ for each minute (or part of a minute) over 100 minutes. a) Write a formula for the company's policy. b) How much is Fred's cell phone bill for the month if he talks for 138 minutes.

What is the range of the function $y=\frac{14}{\sqrt{4-x^{2}}}$ ?

Given $f(x)=4 x^{2}-2$ and $g(x)=-3 x+1$ , find $f(g(5))$ and $g(f(5))$ .

Use the definition of absolute value to write a piecewise formula for $f(x)=\left|3 x^{2}-27\right|$ .

Find the $y$ -coordinate of the point on the graph of $y=h(x)=\frac{1}{\sqrt{x+3}}$ whose $x$ -coordinate is 1 .

Let $C(f(t))$ be a composite function, where $V=f(t)$ is the volume of water, in cubic feet, emitted by a sprinkler system after $t$ minutes, and $C(V)$ is the cost, in dollars, of $V$ cubic feet of water. What are the units of $C(f(t))$ ?

Sketch the graph of $f(x)=(x-4)^{2}+2$

Let $f(x)=\frac{6}{\sqrt{x+21}}$ and $g(x)=x^{2}-10 x$ . Is $x=6$ in the domain of $f(g(x))$ ?

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.45$ for each minute (or part of a minute) over 105 minutes. Which of the following is the domain of the function?