Question 1

Assuming the entire graph of $f(x)$ is shown, what is the domain of $f(x)$ ?

Accepted Answer

A)  $2 \leq x \leq 6$ 
B)  $2 \leq x \leq 10$ 
C)  $2 \leq y \leq 6$ 
D)  $2 \leq y \leq 10$ 
A)  $2 \leq x \leq 6$ 
B)  $2 \leq x \leq 10$ 
C)  $2 \leq y \leq 6$ 
D)  $2 \leq y \leq 10$

Question 2

For $f(x)=x^{2}-4 x+5$, what is $f(x+4)$ ?

Accepted Answer

A)  $x^{2}+12 x-37$ 
B)  $x^{2}-12 x-37$ 
C)  $x^{2}-4 x+5$ 
D)  $x^{2}+4 x+5$ 
A)  $x^{2}+12 x-37$ 
B)  $x^{2}-12 x-37$ 
C)  $x^{2}-4 x+5$ 
D)  $x^{2}+4 x+5$

Question 3

Evaluate $h(0)$ if $h(x)=\left\{\begin{array}{cc}3 x+6, & x \leq-2 \ -x^{2}+4, & x>-2\end{array}\right.$

Accepted Answer

The answer of Evaluate $h(0)$ if \(h(x)=\left\{\begin{array}{cc}3 x+6, & x...

Question 4

Given the function $f(x)=2 x^{2}-6$, find the domain of $f^{-1}(x)$.

Accepted Answer

The answer of Given the function $f(x)=2 x^{2}-6$, find the...

Question 5

Use the following figure to evaluate $f(5)$.

Accepted Answer

The answer of Use the following figure to evaluate $f(5)$.
...

Question 6

Given the following table of values, can you conclude that $f(x)=g(x)$ ?

Accepted Answer

A) True 
 B)False

Question 7

Assume that height is a function of age and that $H=f(a)$ is the average height (in inches) for females in the US at age $a$ years. What is the practical interpretation of $f(z)+10$ ?

Accepted Answer

A)  $z$ plus the number of US females who are 10 inches tall. 
B)  10 plus the number of US females who are $z$ inches tall. 
C)  10 years older than the average US female who is $z$ inches tall. 
D)  10 inches taller than the average height of a $z$ year old US female. 
A)  $z$ plus the number of US females who are 10 inches tall. 
B)  10 plus the number of US females who are $z$ inches tall. 
C)  10 years older than the average US female who is $z$ inches tall. 
D)  10 inches taller than the average height of a $z$ year old US female.

Question 8

Which of the following are not in the domain of $r(x)=\frac{1}{(x+4)^{2}}+\sqrt{3-x}$ ?

Accepted Answer

A) $x=4$ B) $x=-4$ C) $x=3$ D) All numbers $x$ such that $x>3$ E) All numbers $x$ such that $x<3$ A) $x=4$ B) $x=-4$ C) $x=3$ D) All numbers $x$ such that $x>3$ E) All numbers $x$ such that $x<3$

Question 9

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. What does the statement $w(p)=17$ mean?

Accepted Answer

A)  The average $p$-month old girl weighs 17 pounds. 
B)  The average 17-month old girl weighs $p$ pounds. 
C)  There are $p$ baby girls weighing 17 pounds. 
D)  There are 17 baby girls weighing $p$ pounds. 
A)  The average $p$-month old girl weighs 17 pounds. 
B)  The average 17-month old girl weighs $p$ pounds. 
C)  There are $p$ baby girls weighing 17 pounds. 
D)  There are 17 baby girls weighing $p$ pounds.

Question 10

The graph of $f(x)$ is given below. Sketch a graph of $f(x+1)+2$

Accepted Answer

The answer of The graph of $f(x)$ is given below....

Question 11

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 $f(r+6)$.

Accepted Answer

A)  $2 \pi r+6$, the circumference of a circle of radius $r+6$. 
B)  $2 \pi r+6,6$ more than the circumference of a circle of radius $r$. 
C)  $2 \pi r+12 \pi$, the circumference of a circle of radius $r+6$. 
D)  $2 \pi r+12,12$ more than the circumference of a circle of radius $r$. 
A)  $2 \pi r+6$, the circumference of a circle of radius $r+6$. 
B)  $2 \pi r+6,6$ more than the circumference of a circle of radius $r$. 
C)  $2 \pi r+12 \pi$, the circumference of a circle of radius $r+6$. 
D)  $2 \pi r+12,12$ more than the circumference of a circle of radius $r$.

Question 12

If $r(t)=e^{t}$ for $t>0$, what is the formula for $s(t)=r(t-4)$ ?

Accepted Answer

A)  $ s(t)=e^{t-4}$ 
B)  $s(t)=e^{t}-4$ 
C)  $s(t)=e^{t+4}$ 
D)  $s(t)=e^{t}+4$ 
A)  $ s(t)=e^{t-4}$ 
B)  $s(t)=e^{t}-4$ 
C)  $s(t)=e^{t+4}$ 
D)  $s(t)=e^{t}+4$

Question 13

The graph of $g(x)$ contains the point $(3,5)$. Which formula for a translation of $g$ has a graph containing the point $(8,8)$ ?

Accepted Answer

A)  $g(x-5)+3$ 
B)  $ g(x+5)-3$ 
C)  $ g(x-8)+8$ 
D)  $ g(x+8)-8$ 
A)  $g(x-5)+3$ 
B)  $ g(x+5)-3$ 
C)  $ g(x-8)+8$ 
D)  $ g(x+8)-8$

Question 14

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

Accepted Answer

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

Question 15

Let $g(x)=\sqrt{25-x^{2}}$. The range of a function that will translate the graph of $g 6$ units to the right and 2 units up is ---------------$\leq y \leq$------------

Accepted Answer

The answer of Let $g(x)=\sqrt{25-x^{2}}$. The range of a function...

Question 16

If $f$ is decreasing and concave up on $-7\frac{f(-1)-f(-6)}{-1+6}$.

Accepted Answer

A) True 
 B)False

Question 17

The data points for the following table are graphed in the figure below.
   
Is this the graph of a function?

Accepted Answer

A) True 
 B)False

Question 18

Let $f(x)=\frac{1}{x+4}$ with the domain $[-2,3]$. Find the domain of $f^{-1}$.

Accepted Answer

The answer of Let $f(x)=\frac{1}{x+4}$ with the domain $[-2,3]$. Find...

Question 19

Let $f(x)=\frac{2}{x+|x|}$. What is the domain of $f(x)$ ?

Accepted Answer

A)  $ f(x)>2$ 
B)  $ f(x)0$ 
A)  $ f(x)>2$ 
B)  $ f(x)0$

Question 20

Find the domain of the function $g(x)=\sqrt{\frac{3 x}{x-5}}$.

Accepted Answer

All real n

Assuming the entire graph of $f(x)$ is shown, what is the domain of $f(x)$ ?

For $f(x)=x^{2}-4 x+5$ , what is $f(x+4)$ ?

Evaluate $h(0)$ if $h(x)=\left\{\begin{array}{cc}3 x+6, & x \leq-2 \\ -x^{2}+4, & x>-2\end{array}\right.$

Given the function $f(x)=2 x^{2}-6$ , find the domain of $f^{-1}(x)$ .

Use the following figure to evaluate $f(5)$ .

Given the following table of values, can you conclude that $f(x)=g(x)$ ?

Assume that height is a function of age and that $H=f(a)$ is the average height (in inches) for females in the US at age $a$ years. What is the practical interpretation of $f(z)+10$ ?

Which of the following are not in the domain of $r(x)=\frac{1}{(x+4)^{2}}+\sqrt{3-x}$ ?

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. What does the statement $w(p)=17$ mean?

The graph of $f(x)$ is given below. Sketch a graph of $f(x+1)+2$

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 $f(r+6)$ .

If $r(t)=e^{t}$ for $t>0$ , what is the formula for $s(t)=r(t-4)$ ?

The graph of $g(x)$ contains the point $(3,5)$ . Which formula for a translation of $g$ has a graph containing the point $(8,8)$ ?

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

Let $g(x)=\sqrt{25-x^{2}}$ . The range of a function that will translate the graph of $g 6$ units to the right and 2 units up is --------------- $\leq y \leq$ ------------

If $f$ is decreasing and concave up on $-7<x<4$ , then $\frac{f(3)-f(-2)}{3+2}>\frac{f(-1)-f(-6)}{-1+6}$ .

The data points for the following table are graphed in the figure below. Is this the graph of a function?

Let $f(x)=\frac{1}{x+4}$ with the domain $[-2,3]$ . Find the domain of $f^{-1}$ .

Let $f(x)=\frac{2}{x+|x|}$ . What is the domain of $f(x)$ ?

Find the domain of the function $g(x)=\sqrt{\frac{3 x}{x-5}}$ .

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Exam 2: Functions

Assuming the entire graph of f(x)f(x)f(x) is shown, what is the domain of f(x)f(x)f(x) ?

For f(x)=x2−4x+5f(x)=x^{2}-4 x+5f(x)=x2−4x+5 , what is f(x+4)f(x+4)f(x+4) ?

Evaluate h(0)h(0)h(0) if h(x)={3x+6,x≤−2−x2+4,x>−2h(x)=\left\{\begin{array}{cc}3 x+6, & x \leq-2 \\ -x^{2}+4, & x>-2\end{array}\right.h(x)={3x+6,−x2+4,​x≤−2x>−2​

Given the function f(x)=2x2−6f(x)=2 x^{2}-6f(x)=2x2−6 , find the domain of f−1(x)f^{-1}(x)f−1(x) .

Use the following figure to evaluate f(5)f(5)f(5) .

Given the following table of values, can you conclude that f(x)=g(x)f(x)=g(x)f(x)=g(x) ?

Assume that height is a function of age and that H=f(a)H=f(a)H=f(a) is the average height (in inches) for females in the US at age aaa years. What is the practical interpretation of f(z)+10f(z)+10f(z)+10 ?

Which of the following are not in the domain of r(x)=1(x+4)2+3−xr(x)=\frac{1}{(x+4)^{2}}+\sqrt{3-x}r(x)=(x+4)21​+3−x​ ?

Let w(m)w(m)w(m) give the weight (in pounds) of an average-sized baby girl who is mmm months old. What does the statement w(p)=17w(p)=17w(p)=17 mean?

The graph of f(x)f(x)f(x) is given below. Sketch a graph of f(x+1)+2f(x+1)+2f(x+1)+2

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(r+6)f(r+6)f(r+6) .

If r(t)=etr(t)=e^{t}r(t)=et for t>0t>0t>0 , what is the formula for s(t)=r(t−4)s(t)=r(t-4)s(t)=r(t−4) ?

The graph of g(x)g(x)g(x) contains the point (3,5)(3,5)(3,5) . Which formula for a translation of ggg has a graph containing the point (8,8)(8,8)(8,8) ?

Let fff and ggg be two invertible functions such that f−1(x)=3x+3f^{-1}(x)=\frac{3}{x+3}f−1(x)=x+33​ and g(x)=2(x−2)g(x)=2(x-2)g(x)=2(x−2) . Find f(g(5))f(g(5))f(g(5)) . Round your answer to two decimal places, if necessary.

Let g(x)=25−x2g(x)=\sqrt{25-x^{2}}g(x)=25−x2​ . The range of a function that will translate the graph of g6g 6g6 units to the right and 2 units up is --------------- ≤y≤\leq y \leq≤y≤ ------------

If fff is decreasing and concave up on −7<x<4-7<x<4−7<x<4 , then f(3)−f(−2)3+2>f(−1)−f(−6)−1+6\frac{f(3)-f(-2)}{3+2}>\frac{f(-1)-f(-6)}{-1+6}3+2f(3)−f(−2)​>−1+6f(−1)−f(−6)​ .

The data points for the following table are graphed in the figure below. Is this the graph of a function?

Let f(x)=1x+4f(x)=\frac{1}{x+4}f(x)=x+41​ with the domain [−2,3][-2,3][−2,3] . Find the domain of f−1f^{-1}f−1 .

Let f(x)=2x+∣x∣f(x)=\frac{2}{x+|x|}f(x)=x+∣x∣2​ . What is the domain of f(x)f(x)f(x) ?

Find the domain of the function g(x)=3xx−5g(x)=\sqrt{\frac{3 x}{x-5}}g(x)=x−53x​​ .

Linear Functions and Change

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Exponential Functions

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Transformations of Functions and Their Graphs

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Assuming the entire graph of $f(x)$ is shown, what is the domain of $f(x)$ ?

For $f(x)=x^{2}-4 x+5$ , what is $f(x+4)$ ?

Evaluate $h(0)$ if $h(x)=\left\{\begin{array}{cc}3 x+6, & x \leq-2 \\ -x^{2}+4, & x>-2\end{array}\right.$

Given the function $f(x)=2 x^{2}-6$ , find the domain of $f^{-1}(x)$ .

Use the following figure to evaluate $f(5)$ .

Given the following table of values, can you conclude that $f(x)=g(x)$ ?

Assume that height is a function of age and that $H=f(a)$ is the average height (in inches) for females in the US at age $a$ years. What is the practical interpretation of $f(z)+10$ ?

Which of the following are not in the domain of $r(x)=\frac{1}{(x+4)^{2}}+\sqrt{3-x}$ ?

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. What does the statement $w(p)=17$ mean?

The graph of $f(x)$ is given below. Sketch a graph of $f(x+1)+2$

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 $f(r+6)$ .

If $r(t)=e^{t}$ for $t>0$ , what is the formula for $s(t)=r(t-4)$ ?

The graph of $g(x)$ contains the point $(3,5)$ . Which formula for a translation of $g$ has a graph containing the point $(8,8)$ ?

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

Let $g(x)=\sqrt{25-x^{2}}$ . The range of a function that will translate the graph of $g 6$ units to the right and 2 units up is --------------- $\leq y \leq$ ------------

If $f$ is decreasing and concave up on $-7<x<4$ , then $\frac{f(3)-f(-2)}{3+2}>\frac{f(-1)-f(-6)}{-1+6}$ .

Let $f(x)=\frac{1}{x+4}$ with the domain $[-2,3]$ . Find the domain of $f^{-1}$ .

Let $f(x)=\frac{2}{x+|x|}$ . What is the domain of $f(x)$ ?

Find the domain of the function $g(x)=\sqrt{\frac{3 x}{x-5}}$ .