Question 1

If $f(x)=2 x^{2}+4 x$ and $h(x)=f(x)-3$, what is $h(-1)$ ?

Accepted Answer

-5

Question 2

Suppose $f$ and $g$ are invertible functions such that $f(-7)=-12, f(-8)=-14$, $f(-14)=-9, g(-11)=-6, g(-8)=-10$, and $g(-14)=-12$. Find $f^{-1}(g(f(-8)))$.

Accepted Answer

-7

Question 3

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.55$. Let $C(x)$ be the total cost if you need $x$ cans of soda. What is $C(55)$ ?

Accepted Answer

$\$ 15.50$

Question 4

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 $h=f(t)=-4.9 t^{2}+47 t+18$. The range of this function is approximately ---------------$\leq h \leq$------------ Round to the nearest whole number.

Accepted Answer

Part A: 18

Question 5

Which of the following is a piecewise defined function for $f(x)=\frac{|2 x|}{x}$ ?

Accepted Answer

A)  $f(x)= \begin{cases}-2, & x0\end{cases}$ 
B)  $f(x)= \begin{cases}-2, & x \leq 0 \ 2, & x>0\end{cases}$ 
C)  $f(x)=\left\{\begin{array}{cc}-2, & x0\end{array}\right.$ 
D) $f(x)= \begin{cases}-\frac{2}{x}, & x0\end{cases}$ 
A)  $f(x)= \begin{cases}-2, & x0\end{cases}$ 
B)  $f(x)= \begin{cases}-2, & x \leq 0 \ 2, & x>0\end{cases}$ 
C)  $f(x)=\left\{\begin{array}{cc}-2, & x0\end{array}\right.$ 
D) $f(x)= \begin{cases}-\frac{2}{x}, & x0\end{cases}$

Question 6

Which of the following are not in the range of $y=\frac{6-3 x}{7+x}$ ?

Accepted Answer

A) $y=2$ B) $y=-7$ C) $y=-3$ D) All numbers $y$ such that $y>-7$ E) All numbers y such that $y<-7$ A) $y=2$ B) $y=-7$ C) $y=-3$ D) All numbers $y$ such that $y>-7$ E) All numbers y such that $y<-7$

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 $f(20)$ ?

Accepted Answer

A)  The number of US females who are 20 years old. 
B)  The number of US females who are 20 inches tall. 
C)  The average height of a US female who is 20 years old. 
D)  The average age of a US female who is 20 inches tall. 
A)  The number of US females who are 20 years old. 
B)  The number of US females who are 20 inches tall. 
C)  The average height of a US female who is 20 years old. 
D)  The average age of a US female who is 20 inches tall.

Question 8

Calculate successive rates of change for the function $f(x)$ shown in the following table to determine if the graph is more likely concave up or concave down for $0.1 \leq x \leq 0.4$.

Accepted Answer

A)  concave down 
B)  concave up 
C)  neither 
A)  concave down 
B)  concave up 
C)  neither

Question 9

Find the inverse for the function $y=f(x)=4 x+3$.

Accepted Answer

A) $f^{-1}(x)=\frac{x}{4}-3$ 
B)  $f^{-1}(x)=4 x-3$ 
C)  $f^{-1}(x)=\frac{x-3}{4}$ 
D)  $f^{-1}(x)=\frac{x-4}{3}$ 
A) $f^{-1}(x)=\frac{x}{4}-3$ 
B)  $f^{-1}(x)=4 x-3$ 
C)  $f^{-1}(x)=\frac{x-3}{4}$ 
D)  $f^{-1}(x)=\frac{x-4}{3}$

Question 10

Let $f(x)=\ln x$ and $g(x)=\ln (x)+5$ for $x>0$. How does the graph of $g(x)$ compare to the graph of $f(x)$ ?

Accepted Answer

A)  The graph of $g(x)$ is 5 units up. 
B)  The graph of $g(x)$ is 5 units down. 
C)  The graph of $g(x)$ is 5 units to the right. 
D)  The graph of $g(x)$ is 5 units to the left. 
A)  The graph of $g(x)$ is 5 units up. 
B)  The graph of $g(x)$ is 5 units down. 
C)  The graph of $g(x)$ is 5 units to the right. 
D)  The graph of $g(x)$ is 5 units to the left.

Question 11

Let $g(x)=\sqrt{16-x^{2}}$. Which of the following functions will translate the graph of $g 3$ units to the left and 6 units down?

Accepted Answer

A)  $ h(x)=\sqrt{16-(x-3)^{2}}-6$ 
B)  $ h(x)=\sqrt{16-(x-3)^{2}}+6$ 
C)  $ h(x)=\sqrt{16-(x+3)^{2}}-6$ 
D)  $h(x)=\sqrt{16-(x+3)^{2}}+6$ 
A)  $ h(x)=\sqrt{16-(x-3)^{2}}-6$ 
B)  $ h(x)=\sqrt{16-(x-3)^{2}}+6$ 
C)  $ h(x)=\sqrt{16-(x+3)^{2}}-6$ 
D)  $h(x)=\sqrt{16-(x+3)^{2}}+6$

Question 12

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

Accepted Answer

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

Question 13

Find the inverse for the function $y=f(x)=3 x+6$.

Accepted Answer

The answer of Find the inverse for the function \(y=f(x)=3...

Question 14

Let $f(x)=\frac{4}{\sqrt{x+36}}$ and $g(x)=x^{2}-13 x$. Find the domain of $f(g(x))$.

Accepted Answer

All real n

Question 15

For a given function $f(x)$, suppose $g(x)=f(x-1)$ and $h(x)=f(x)-1$. All three functions are graphed below. Which curve shows the graph of $h$ ?

Accepted Answer

The answer of For a given function $f(x)$, suppose $g(x)=f(x-1)$...

Question 16

A bowling alley charges $\$ 2.60$ for shoes plus $\$ 2.75$ per game bowled. Let $C(g)$ be the total cost for bowling $g$ games (including shoe rental). Now suppose the bowling alley decides to increase the cost for shoes by $\$ 2.00$ and include the first game for free. What is the formula for the new total cost, $N(g)$, of bowling $g$ games as a transformation of $C(g)$ ?

Accepted Answer

A)  $ N(g)=C(g-2.75)+4.60$ 
B)  $ N(g)=C(g-1)+2.00$ 
C)  $ N(g)=C(g-1)+4.60$ 
D)  $ N(g)=C(g+1.75)+2.00$ 
A)  $ N(g)=C(g-2.75)+4.60$ 
B)  $ N(g)=C(g-1)+2.00$ 
C)  $ N(g)=C(g-1)+4.60$ 
D)  $ N(g)=C(g+1.75)+2.00$

Question 17

The data points for the following table are graphed in the figure below.
 
For the graph that is a function, what is its domain?

Accepted Answer

A)  $-1 \leq s \leq 6$ 
B)  $1 \leq t \leq 5$ 
A)  $-1 \leq s \leq 6$ 
B)  $1 \leq t \leq 5$

Question 18

Given $g(x)=4 x^{2}-5 x$, what is $g(5-x)$ ?

Accepted Answer

A)  $-4 x^{2}+35 x-75$ 
B)  $-4 x^{2}-35 x+75$ 
C)  $4 x^{2}+35 x-75$ 
D)  $4 x^{2}-35 x+75$ 
A)  $-4 x^{2}+35 x-75$ 
B)  $-4 x^{2}-35 x+75$ 
C)  $4 x^{2}+35 x-75$ 
D)  $4 x^{2}-35 x+75$

Question 19

If $r(t)=e^{t}$ for $t>0$, what is the formula for $s(t)=r(t)-3$ ?

Accepted Answer

A)  $s(t)=e^{t-3}$ 
B)  $s(t)=e^{t}-3$ 
C)  $s(t)=e^{t+3}$ 
D)  $s(t)=e^{t}+3$ 
A)  $s(t)=e^{t-3}$ 
B)  $s(t)=e^{t}-3$ 
C)  $s(t)=e^{t+3}$ 
D)  $s(t)=e^{t}+3$

Question 20

A T-shirt printing company charges a set-up fee of $\$ 15$ for each order, plus the cost per shirt shown in the table.
  
Let $C$ be the total cost in dollars for printing $n$ shirts. Which of the following is the formula for $C$ ?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

If $f(x)=2 x^{2}+4 x$ and $h(x)=f(x)-3$ , what is $h(-1)$ ?

Suppose $f$ and $g$ are invertible functions such that $f(-7)=-12, f(-8)=-14$ , $f(-14)=-9, g(-11)=-6, g(-8)=-10$ , and $g(-14)=-12$ . Find $f^{-1}(g(f(-8)))$ .

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.55$ . Let $C(x)$ be the total cost if you need $x$ cans of soda. What is $C(55)$ ?

Which of the following is a piecewise defined function for $f(x)=\frac{|2 x|}{x}$ ?

Which of the following are not in the range of $y=\frac{6-3 x}{7+x}$ ?

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 $f(20)$ ?

Find the inverse for the function $y=f(x)=4 x+3$ .

Let $f(x)=\ln x$ and $g(x)=\ln (x)+5$ for $x>0$ . How does the graph of $g(x)$ compare to the graph of $f(x)$ ?

Let $g(x)=\sqrt{16-x^{2}}$ . Which of the following functions will translate the graph of $g 3$ units to the left and 6 units down?

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

Find the inverse for the function $y=f(x)=3 x+6$ .

Let $f(x)=\frac{4}{\sqrt{x+36}}$ and $g(x)=x^{2}-13 x$ . Find the domain of $f(g(x))$ .

For a given function $f(x)$ , suppose $g(x)=f(x-1)$ and $h(x)=f(x)-1$ . All three functions are graphed below. Which curve shows the graph of $h$ ?

The data points for the following table are graphed in the figure below. For the graph that is a function, what is its domain?

Given $g(x)=4 x^{2}-5 x$ , what is $g(5-x)$ ?

If $r(t)=e^{t}$ for $t>0$ , what is the formula for $s(t)=r(t)-3$ ?

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Exam 2: Functions

If f(x)=2x2+4xf(x)=2 x^{2}+4 xf(x)=2x2+4x and h(x)=f(x)−3h(x)=f(x)-3h(x)=f(x)−3 , what is h(−1)h(-1)h(−1) ?

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $1.55\$ 1.55$1.55 . Let C(x)C(x)C(x) be the total cost if you need xxx cans of soda. What is C(55)C(55)C(55) ?

Which of the following is a piecewise defined function for f(x)=∣2x∣xf(x)=\frac{|2 x|}{x}f(x)=x∣2x∣​ ?

Which of the following are not in the range of y=6−3x7+xy=\frac{6-3 x}{7+x}y=7+x6−3x​ ?

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(20)f(20)f(20) ?

Calculate successive rates of change for the function f(x)f(x)f(x) shown in the following table to determine if the graph is more likely concave up or concave down for 0.1≤x≤0.40.1 \leq x \leq 0.40.1≤x≤0.4 .

Find the inverse for the function y=f(x)=4x+3y=f(x)=4 x+3y=f(x)=4x+3 .

Let f(x)=ln⁡xf(x)=\ln xf(x)=lnx and g(x)=ln⁡(x)+5g(x)=\ln (x)+5g(x)=ln(x)+5 for x>0x>0x>0 . How does the graph of g(x)g(x)g(x) compare to the graph of f(x)f(x)f(x) ?

Let g(x)=16−x2g(x)=\sqrt{16-x^{2}}g(x)=16−x2​ . Which of the following functions will translate the graph of g3g 3g3 units to the left and 6 units down?

Let fff and ggg be two invertible functions such that f−1(x)=4x+4f^{-1}(x)=\frac{4}{x+4}f−1(x)=x+44​ and g(x)=3(x−2)g(x)=3(x-2)g(x)=3(x−2) . Find f(g−1(5))f\left(g^{-1}(5)\right)f(g−1(5)) . Round your answer to two decimal places, if necessary.

Find the inverse for the function y=f(x)=3x+6y=f(x)=3 x+6y=f(x)=3x+6 .

Let f(x)=4x+36f(x)=\frac{4}{\sqrt{x+36}}f(x)=x+36​4​ and g(x)=x2−13xg(x)=x^{2}-13 xg(x)=x2−13x . Find the domain of f(g(x))f(g(x))f(g(x)) .

For a given function f(x)f(x)f(x) , suppose g(x)=f(x−1)g(x)=f(x-1)g(x)=f(x−1) and h(x)=f(x)−1h(x)=f(x)-1h(x)=f(x)−1 . All three functions are graphed below. Which curve shows the graph of hhh ?

The data points for the following table are graphed in the figure below. For the graph that is a function, what is its domain?

Given g(x)=4x2−5xg(x)=4 x^{2}-5 xg(x)=4x2−5x , what is g(5−x)g(5-x)g(5−x) ?

If r(t)=etr(t)=e^{t}r(t)=et for t>0t>0t>0 , what is the formula for s(t)=r(t)−3s(t)=r(t)-3s(t)=r(t)−3 ?

A T-shirt printing company charges a set-up fee of $15\$ 15$15 for each order, plus the cost per shirt shown in the table. Let CCC be the total cost in dollars for printing nnn shirts. Which of the following is the formula for CCC ?

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

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If $f(x)=2 x^{2}+4 x$ and $h(x)=f(x)-3$ , what is $h(-1)$ ?

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.55$ . Let $C(x)$ be the total cost if you need $x$ cans of soda. What is $C(55)$ ?

Which of the following is a piecewise defined function for $f(x)=\frac{|2 x|}{x}$ ?

Which of the following are not in the range of $y=\frac{6-3 x}{7+x}$ ?

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 $f(20)$ ?

Find the inverse for the function $y=f(x)=4 x+3$ .

Let $f(x)=\ln x$ and $g(x)=\ln (x)+5$ for $x>0$ . How does the graph of $g(x)$ compare to the graph of $f(x)$ ?

Let $g(x)=\sqrt{16-x^{2}}$ . Which of the following functions will translate the graph of $g 3$ units to the left and 6 units down?

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

Find the inverse for the function $y=f(x)=3 x+6$ .

Let $f(x)=\frac{4}{\sqrt{x+36}}$ and $g(x)=x^{2}-13 x$ . Find the domain of $f(g(x))$ .

For a given function $f(x)$ , suppose $g(x)=f(x-1)$ and $h(x)=f(x)-1$ . All three functions are graphed below. Which curve shows the graph of $h$ ?

Given $g(x)=4 x^{2}-5 x$ , what is $g(5-x)$ ?

If $r(t)=e^{t}$ for $t>0$ , what is the formula for $s(t)=r(t)-3$ ?