Question 1

$\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x ) + 4 \text {. }$

Accepted Answer

A) 
 
B) 
 
C) 
 
D) 
 
E)

Question 2

Determine whether the function is even, odd, or neither. $f ( x ) = x \sin 2 x$

Accepted Answer

A)  even 
B)  odd 
C)  neither

Question 3

$$\text { Which of the following is the correct graph of } y = 3 x - x ^ { 2 } \text { ? }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D) 
 
E)

Question 4

Table given below shows the Consumer Price Index (CPI) for selected years. The mathematical model for the data given below is $y = - 0.031 t ^ { 2 } + 5.887 t + 24.429$, where $y$ represents the CPI and $t$ represents the year, with $t = 5$ corresponding to 1975 . Use the model to predict the CPI for the year 2010. Round your answer to the nearest integer.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \text { ear } & 975 & 980 & 985 & 990 & 995 & 000 & 005 \
\hline \text { PI } & 2.8 & 0 & 06.6 & 30.7 & 52.4 & 71.2 & 94.3 \
\hline
\end{array}$

Accepted Answer

A)  $y = 211$ 
B)  $y = 209$ 
C)  $y = 192$ 
D)  $y = 173$ 
E)  $y = 210$

Question 5

all intercepts: $$y = ( x + 5 ) \sqrt { 4 - x ^ { 2 } }$$

Accepted Answer

A)  $x$-intercepts: $( - 5,0 ) , ( - 2,0 ) , ( 2,0 ) ; y$-intercepts: $( 0,0 ) , ( 0,10 )$ 
B)  $x$-intercepts: $( - 5,0 ) , ( 2,0 ) ; y$-intercept: $( 0,10 )$ 
C)  $x$-intercepts: $( - 5,0 ) , ( 2,0 ) ; y$-intercept: $( 0 , - 10 )$ 
D)  $x$-intercepts: $( - 5,0 ) , ( - 2,0 ) , ( 2,0 ) ; y$-intercept: $( 0,10 )$ 
E)  $x$-intercepts: $( - 5,0 ) , ( - 2,0 ) , ( 2,0 ) ; y$-intercept: $( 0 , - 10 )$

Question 6

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } }$

Accepted Answer

A) $f ^ { - 1 } ( x ) = \frac { 17 } { 7 } ^ { \frac { 7 } { 17 } }$ 
B) $f ^ { - 1 } ( x ) = x ^ { - \frac { 7 } { 17 } }$ 
C)  $f ^ { - 1 } ( x ) = x ^ { 119 }$ 
D) $f ^ { - 1 } ( x ) = x ^ { - \frac { 17 } { 7 } }$ 
E) $f^{-1}(x)=x^{\frac{17}{7}}$

Question 7

Let $g ( x ) = \frac { 1 } { \sqrt { x + 15 } }$.
Evaluate the expression $\frac { g ( x ) - g ( - 11 ) } { x + 11 }$ and then simplify the result. $g ( x ) = \frac { 1 } { \sqrt { x + 15 } } , \frac { g ( x ) - g ( - 11 ) } { x + 11 }$

Accepted Answer

A)  $\frac { 2 \sqrt { x + 15 } - x - 15 } { 2 ( x + 11 ) ( x + 15 ) }$ 
B)  $\frac { 2 \sqrt { x + 15 } + x - 15 } { 2 ( x - 11 ) ( x + 15 ) }$ 
C)  $\frac { 2 \sqrt { x + 15 } + x - 15 } { 2 ( x + 11 ) ( x + 15 ) }$ 
D)  $\frac { 2 \sqrt { x + 15 } - x - 15 } { 2 ( x - 11 ) ( x + 15 ) }$ 
E)  undefined

Question 8

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x )$ $ =3 \sqrt[5]{8 x-9} $

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 1 } { 3 } ( 8 x - 9 ) ^ { 5 }$ 
B) $f ^ { - 1 } ( x ) = \frac { 1 } { 3 } \left( \left( \frac { x } { 3 } \right) ^ { 5 } + 9 \right)$ 
C) $f ^ { - 1 } ( x ) = \frac { 1 } { 8 } \left( \left( \frac { x } { 3 } \right) ^ { 5 } - 9 \right)$ 
D) $f ^ { - 1 } ( x ) = \frac { 1 } { 8 } \left( \left( \frac { x } { 3 } \right) ^ { 5 } + 9 \right)$ 
E)  $f ^ { - 1 } ( x )$ does not exist

Question 9

$\text { Find the slope of the line passing through the points } \left( - \frac { 1 } { 8 } , \frac { 8 } { 3 } \right) \text { and } \left( - \frac { 3 } { 16 } , \frac { 1 } { 24 } \right) \text {. }$

Accepted Answer

A)  63 
B)  $- 21$ 
C)  42 
D)  21 
E)  $- 42$

Question 10

$\text { A real estate office handles an apartment complex with } 50 \text { units. When the rent is }$ $\$ 800$ per month, all 50 units are occupied. However, when the rent is $\$ 845$, the average number of occupied units drops to 47 . Assume that the relationship between the monthly rent $p$ and the demand $x$ is linear. Write a linear equation giving the demand $x$ in terms of the rent $p$.

Accepted Answer

A)  $x = \frac { 1 } { 15 } ( 1595 - p )$ 
B)  $x = \frac { 1 } { 15 } ( 1505 + p )$ 
C)  $x = \frac { 1 } { 45 } ( 1550 + p )$ 
D)  $x = \frac { 1 } { 15 } ( 1550 - p )$ 
E)  $x = \frac { 1 } { 45 } ( 1595 - p )$

Question 11

The resistance $y$ in ohms of 1000 feet of solid metal wire at $77$ $F^{\circ}$ can be approximated by the model $y = \frac { 12,750 } { x ^ { 2 } } - 0.37,5 \leq x \leq 100$, where $x$ is the diameter of the wire in mils $( 0.001$ in $)$. If the diameter of the wire is doubled, the resistance is changed by approximately what factor? In determining your answer, you can ignore the constant $- 0.37$.

Accepted Answer

A)  3 
B)  $\frac { 1 } { 2 }$ 
C)  4 
D)  $\frac { 1 } { 4 }$ 
E)  $\frac { 1 } { 3 }$

Question 12

$$\text { Find the domain and range of the function } h ( x ) = \frac { 11 } { x + 6 } \text {. }$$

Accepted Answer

A)  domain: $( - \infty , - 6 ) \cup ( - 6 , \infty )$
 range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , - 6 ) \cup ( - 6 , \infty )$ 
range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , - 6 ] \cup [ - 6 , \infty )$ 
range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  domain: $( - \infty , - 6 )$
range: $( 0 , \infty )$ 
E)  domain: $( - 6 , \infty )$
range: $( 0 , \infty )$

Question 13

$\text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. }$

Accepted Answer

A)  $t ^ { 3 } - 4 t ^ { 2 } + 12 t - 144$ 
B)  $t ^ { 3 } - 4 t ^ { 2 } + 84 t - 144$ 
C)  $t ^ { 3 } - 16 t ^ { 2 } + 84 t - 144$ 
D)  $t ^ { 3 } - 16 t ^ { 2 } + 12 t - 144$ 
E)  none of the above

Question 14

Find the coordinates of a second point on the graph of a function f if the given point $\left( - \frac { 9 } { 8 } , 5 \right)$ is on the graph and the function is odd.

Accepted Answer

A)  $\left( - 5 , - \frac { 9 } { 8 } \right)$ 
B)  $\left( \frac { 9 } { 8 } , - 5 \right)$ 
C)  $\left( - 5 , \frac { 9 } { 8 } \right)$ 
D)  $\left( - \frac { 9 } { 8 } , - 5 \right)$ 
E)  $\left( \frac { 9 } { 8 } , 5 \right)$

Question 15

$\text { Find the domain and range of the function } g ( t ) = \sqrt { t - 10 } \text {. }$

Accepted Answer

A)  domain: $[ 10 , \infty )$ 
range: $( 0 , \infty )$ 
B)  domain: $( 10 , \infty )$
 range: $[ 0 , \infty )$ 
C)  domain: $[ 10 , \infty )$ 
range: $( - \infty , \infty )$ 
D)  domain: $[ 0 , \infty )$ 
range: $[ 10 , \infty )$ 
E)  none of the above

Question 16

You need 50 pounds of two commodities costing $1.60 and $1.95 per pound. Determine the number of pounds of the less expensive commodity purchased if the total cost $y = 1.60 x + 1.95 ( 50 - x )$ is $\$ 94$.

Accepted Answer

A)  10 pounds 
B)  17 pounds 
C)  7 pounds 
D)  5 pounds 
E)  13 pounds

Question 17

$$\text { What is the domain of the function } f ( x ) = 6 \ln ( 4 x ) ?$$

Accepted Answer

A)  $( 0 , \infty )$ 
B)  $\left( \frac { 1 } { 4 } \infty \right)$ 
C)  $( 0,1 )$ 
D)  $( 1 , e )$ 
E)  $( e , \infty )$

Question 18

Hooke's Law states that the force F required to compress or stretch a spring (within its elastic limits) is proportional to the distance $d$ that the spring is compressed or stretched from its original length. That is, $F = k d$ where $k$ is a measure of the stiffness of the spring and is called the spring constant. The table shows the elongation $d$ in centimeters of a spring when a force of $F$ newtons is applied. Use a graphing utility to plot the data and graph the linear model.
$\begin{array}{|l|c|c|c|c|c|}
\hline F & 20 & 40 & 60 & 80 & 100 \
\hline d & 1.3 & 2.6 & 3.9 & 5.2 & 6.5 \
\hline
\end{array}$

Accepted Answer

A) 
 
B) 
 
C) 
 
D) 
 
E)

Question 19

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 6 x ^ { 2 } , x \geq 0 \text {. }$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { \frac { 1 } { 6 x } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { 6 x ^ { 2 } }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { \frac { 6 } { x } }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { 6 \sqrt { x } }$ 
E) $f ^ { - 1 } ( x ) = \sqrt { \frac { x } { 6 } }$

Question 20

$\text { Solve the following equation for } x \text {. }$ $- 5 + 7 e ^ { 3 x } = 10$

Accepted Answer

A)  $x = \frac { 1 } { 3 } \ln \frac { 15 } { 7 }$ 
B)  $x = - \frac { 1 } { 3 } \ln \frac { 15 } { 7 }$ 
C)  $x = \frac { 15 } { 7 e ^ { 3 } }$ 
D)  $x = - \frac { 1 } { 3 } \ln \frac { 50 } { 7 }$ 
E)  $x = \frac { 1 } { 3 } \ln \frac { 50 } { 7 }$

Exam 1: Graphs and Models

$\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x ) + 4 \text {. }$ $\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x ) + 4 \text {. } A) B) C) D) E)$

Determine whether the function is even, odd, or neither. $f ( x ) = x \sin 2 x$

$\text { Which of the following is the correct graph of } y = 3 x - x ^ { 2 } \text { ? }$

all intercepts: $y = ( x + 5 ) \sqrt { 4 - x ^ { 2 } }$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } }$

Let $g ( x ) = \frac { 1 } { \sqrt { x + 15 } }$ . Evaluate the expression $\frac { g ( x ) - g ( - 11 ) } { x + 11 }$ and then simplify the result. $g ( x ) = \frac { 1 } { \sqrt { x + 15 } } , \frac { g ( x ) - g ( - 11 ) } { x + 11 }$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x )$ $=3 \sqrt[5]{8 x-9}$

$\text { Find the slope of the line passing through the points } \left( - \frac { 1 } { 8 } , \frac { 8 } { 3 } \right) \text { and } \left( - \frac { 3 } { 16 } , \frac { 1 } { 24 } \right) \text {. }$

$\text { Find the domain and range of the function } h ( x ) = \frac { 11 } { x + 6 } \text {. }$

$\text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. }$

Find the coordinates of a second point on the graph of a function f if the given point $\left( - \frac { 9 } { 8 } , 5 \right)$ is on the graph and the function is odd.

$\text { Find the domain and range of the function } g ( t ) = \sqrt { t - 10 } \text {. }$

You need 50 pounds of two commodities costing $1.60 and $1.95 per pound. Determine the number of pounds of the less expensive commodity purchased if the total cost $y = 1.60 x + 1.95 ( 50 - x )$ is $\$ 94$ .

$\text { What is the domain of the function } f ( x ) = 6 \ln ( 4 x ) ?$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 6 x ^ { 2 } , x \geq 0 \text {. }$

$\text { Solve the following equation for } x \text {. }$ $- 5 + 7 e ^ { 3 x } = 10$

Exam 1: Graphs and Models

Use the graph of y=f(x) given below to find the graph of the function y=f(x) +4. \text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x ) + 4 \text {. } Use the graph of y=f(x) given below to find the graph of the function y=f(x) +4.

Determine whether the function is even, odd, or neither. f(x) =xsin⁡2xf ( x ) = x \sin 2 xf(x) =xsin2x

Which of the following is the correct graph of y=3x−x2 ? \text { Which of the following is the correct graph of } y = 3 x - x ^ { 2 } \text { ? } Which of the following is the correct graph of y=3x−x2 ?

all intercepts: y=(x+5) 4−x2y = ( x + 5 ) \sqrt { 4 - x ^ { 2 } }y=(x+5) 4−x2​

Find f−1(x) if f(x) =x717\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } } Find f−1(x) if f(x) =x177​

Find f−1(x) if f(x) \text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) Find f−1(x) if f(x) =38x−95 =3 \sqrt[5]{8 x-9} =358x−9​

Find the domain and range of the function h(x) =11x+6. \text { Find the domain and range of the function } h ( x ) = \frac { 11 } { x + 6 } \text {. } Find the domain and range of the function h(x) =x+611​.

Evaluate (if possible) the function g(x) =x2(x+2) at x=t−6. Simplify the result. \text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. } Evaluate (if possible) the function g(x) =x2(x+2) at x=t−6. Simplify the result.

Find the coordinates of a second point on the graph of a function f if the given point (−98,5) \left( - \frac { 9 } { 8 } , 5 \right) (−89​,5) is on the graph and the function is odd.

Find the domain and range of the function g(t) =t−10. \text { Find the domain and range of the function } g ( t ) = \sqrt { t - 10 } \text {. } Find the domain and range of the function g(t) =t−10​.

You need 50 pounds of two commodities costing $1.60 and $1.95 per pound. Determine the number of pounds of the less expensive commodity purchased if the total cost y=1.60x+1.95(50−x) y = 1.60 x + 1.95 ( 50 - x ) y=1.60x+1.95(50−x) is $94\$ 94$94 .

What is the domain of the function f(x) =6ln⁡(4x) ?\text { What is the domain of the function } f ( x ) = 6 \ln ( 4 x ) ? What is the domain of the function f(x) =6ln(4x) ?

Find f−1(x) if f(x) =6x2,x≥0. \text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 6 x ^ { 2 } , x \geq 0 \text {. } Find f−1(x) if f(x) =6x2,x≥0.

Solve the following equation for x. \text { Solve the following equation for } x \text {. } Solve the following equation for x. −5+7e3x=10- 5 + 7 e ^ { 3 x } = 10−5+7e3x=10

$\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x ) + 4 \text {. }$ $\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x ) + 4 \text {. } A) B) C) D) E)$

Determine whether the function is even, odd, or neither. $f ( x ) = x \sin 2 x$

$\text { Which of the following is the correct graph of } y = 3 x - x ^ { 2 } \text { ? }$

all intercepts: $y = ( x + 5 ) \sqrt { 4 - x ^ { 2 } }$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } }$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x )$ $=3 \sqrt[5]{8 x-9}$

$\text { Find the domain and range of the function } h ( x ) = \frac { 11 } { x + 6 } \text {. }$

$\text { Evaluate (if possible) the function } g ( x ) = x ^ { 2 } ( x + 2 ) \text { at } x = t - 6 \text {. Simplify the result. }$

Find the coordinates of a second point on the graph of a function f if the given point $\left( - \frac { 9 } { 8 } , 5 \right)$ is on the graph and the function is odd.

$\text { Find the domain and range of the function } g ( t ) = \sqrt { t - 10 } \text {. }$

You need 50 pounds of two commodities costing $1.60 and $1.95 per pound. Determine the number of pounds of the less expensive commodity purchased if the total cost $y = 1.60 x + 1.95 ( 50 - x )$ is $\$ 94$ .

$\text { What is the domain of the function } f ( x ) = 6 \ln ( 4 x ) ?$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 6 x ^ { 2 } , x \geq 0 \text {. }$

$\text { Solve the following equation for } x \text {. }$ $- 5 + 7 e ^ { 3 x } = 10$