Question 1

$\text { Find the } y \text {-intercept of the line } x + 4 y = 8 \text {. }$

Accepted Answer

A)  $( 0,2 )$ 
B)  $( 0,4 )$ 
C)  $( 0,8 )$ 
D)  $( 4,0 )$ 
E)  $( 2,0 )$ 
A)  $( 0,2 )$ 
B)  $( 0,4 )$ 
C)  $( 0,8 )$ 
D)  $( 4,0 )$ 
E)  $( 2,0 )$

Question 2

$$\text { Let } f ( x ) = 14 x + 8 \text {. Then simplify the expression } \frac { f ( x ) - f ( 9 ) } { x - 9 } \text {. }$$

Accepted Answer

A)  15 
B)  14 
C)  19 
D)  11 
E)  undefined 
A)  15 
B)  14 
C)  19 
D)  11 
E)  undefined

Question 3

$\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x + 5 ) \text {. }$

Accepted Answer

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

Question 4

V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds $x$ (in thousands of revolutions per minute). The results are shown in the table below. Use the regression capabilities of a graphing utility to find a cubic model for the data. Round the numerical values in your answer to three decimal places, where applicable.
$\begin{array}{|c|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline y & 64 & 109 & 164 & 224 & 249 & 269 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 1.608 x ^ { 3 } - 14.583 x ^ { 2 } + 13.389 x - 37$ 
B)  $y = - 1.706 x ^ { 3 } - 14.583 x ^ { 2 } - 16.389 x + 34$ 
C)  $y = 1.806 x ^ { 3 } + 11.583 x ^ { 2 } + 16.389 x - 41$ 
D)  $y = - 1.806 x ^ { 3 } + 14.583 x ^ { 2 } + 16.389 x + 34$ 
E)  $y = 1.608 x ^ { 3 } + 11.583 x ^ { 2 } - 19.389 x + 41$ 
A)  $y = - 1.608 x ^ { 3 } - 14.583 x ^ { 2 } + 13.389 x - 37$ 
B)  $y = - 1.706 x ^ { 3 } - 14.583 x ^ { 2 } - 16.389 x + 34$ 
C)  $y = 1.806 x ^ { 3 } + 11.583 x ^ { 2 } + 16.389 x - 41$ 
D)  $y = - 1.806 x ^ { 3 } + 14.583 x ^ { 2 } + 16.389 x + 34$ 
E)  $y = 1.608 x ^ { 3 } + 11.583 x ^ { 2 } - 19.389 x + 41$

Question 5

$\text { A real estate office handles an apartment complex with } 50 \text { units. When the rent is }$ $\$ 600$ per month, all 50 units are occupied. However, when the rent is $\$ 645$, the average number of occupied units drops to 47 . Assume that the relationship between the monthly rent $p$ and the demand $x$ is linear. Predict the number of units occupied if the rent is raised to $\$ 660$.

Accepted Answer

A)  43 units 
B)  54 units 
C)  57 units 
D)  49 units 
E)  46 units 
A)  43 units 
B)  54 units 
C)  57 units 
D)  49 units 
E)  46 units

Question 6

$\text { A company reimburses its sales representatives } \$ 160 \text { per day for lodging and meals }$ plus 42 e per mile driven. How much does it cost the company if a sales representative drives 135 miles on a given day? Round your answer to the nearest cent.

Accepted Answer

A)  $227.20$ 
B)  $216.70$ 
C)  $136.35$ 
D)  $161.35$ 
E)  $191.70$ 
A)  $227.20$ 
B)  $216.70$ 
C)  $136.35$ 
D)  $161.35$ 
E)  $191.70$

Question 7

Which function below would be most appropriate model for the given data?

Accepted Answer

A) no apparent relationship between x and y 
B) trigonometric 
C) quadratic 
D) linear 
A) no apparent relationship between x and y 
B) trigonometric 
C) quadratic 
D) linear

Question 8

V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds $x$ (in thousands of revolutions per minute). The results are shown in the table below. Use the model $y = - 1.806 x ^ { 3 } + 14.58 x ^ { 2 } + 16.4 x + 30$ to approximate the horsepower when the engine is running at 5500 revolutions per minute. Round your answer to two decimal places.
$\begin{array}{|c|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline y & 60 & 105 & 160 & 220 & 245 & 265 \
\hline
\end{array}$

Accepted Answer

A)  $260.77 \mathrm { hp }$ 
B)  $262.73 \mathrm { hp }$ 
C)  $262.36 \mathrm { hp }$ 
D)  $261.38 \mathrm { hp }$ 
E)  $261.91 \mathrm { hp }$ 
A)  $260.77 \mathrm { hp }$ 
B)  $262.73 \mathrm { hp }$ 
C)  $262.36 \mathrm { hp }$ 
D)  $261.38 \mathrm { hp }$ 
E)  $261.91 \mathrm { hp }$

Question 9

$\text { A company reimburses its sales representatives } \$ 175 \text { per day for lodging and meals }$ plus $45 \&$ per mile driven. Write a linear equation giving the daily cost $C$ to the company in terms of $x$, the number of miles driven. Round the numerical values in your answer to two decimal places, where applicable.

Accepted Answer

A)  $C = - 1.75 x + 45$ 
B)  $C = 0.45 x + 175$ 
C)  $C = - 0.45 x - 175$ 
D)  $C = 0.45 x - 175$ 
E)  $C = 1.75 x - 45$ 
A)  $C = - 1.75 x + 45$ 
B)  $C = 0.45 x + 175$ 
C)  $C = - 0.45 x - 175$ 
D)  $C = 0.45 x - 175$ 
E)  $C = 1.75 x - 45$

Question 10

$\text { Find an equation of the line through the points of intersection of } y = x ^ { 2 } \text { and }$ $y = 6 x - x ^ { 2 }$

Accepted Answer

A)  $y = x - 6$ 
B)  $y = 6 x$ 
C)  $y = - 6 x$ 
D)  $y = 3 x$ 
E)  $y = x + 3$ 
A)  $y = x - 6$ 
B)  $y = 6 x$ 
C)  $y = - 6 x$ 
D)  $y = 3 x$ 
E)  $y = x + 3$

Question 11

$\text { Given } f ( x ) = \cos x \text { and } g ( x ) = \frac { \pi } { 2 } x \text {, evaluate } f ( g ( 2 ) )$

Accepted Answer

A)  0 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \pi } { 2 } \sin ( 2 )$ 
D)  $- 1$ 
E)  $\frac { \pi } { 2 } \cos ( 2 )$ 
A)  0 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \pi } { 2 } \sin ( 2 )$ 
D)  $- 1$ 
E)  $\frac { \pi } { 2 } \cos ( 2 )$

Question 12

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 the regression capabilities of a graphing utility to find a linear model for the data. Round the numerical values in your answer to three decimal places.
$\begin{array}{|c|c|c|c|c|c|}
\hline F & 20 & 40 & 60 & 80 & 100 \
\hline d & 1.9 & 3.8 & 5.7 & 7.6 & 9.5 \
\hline
\end{array}$

Accepted Answer

A)  $d = 0.675 F$ 
B)  $d = 0.118 \mathrm {~F}$ 
C)  $d = 0.112 F$ 
D)  $d = 0.095 F$ 
E)  $d = 0.905 F$ 
A)  $d = 0.675 F$ 
B)  $d = 0.118 \mathrm {~F}$ 
C)  $d = 0.112 F$ 
D)  $d = 0.095 F$ 
E)  $d = 0.905 F$

Question 13

$\text { An open box of maximum volume is to be made from a square piece of material } 22$
centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). Write the volume $V \text { as a function of } x \text {, the length of the corner squares. }$

Accepted Answer

A)  $V = x ( 22 - 2 x ) ^ { 2 }$ 
B)  $V = x + ( 22 - x ) ^ { 2 }$ 
C)  $V = x ^ { 2 } + ( 22 - 2 x )$ 
D)  $V = x ^ { 2 } ( 22 - 2 x )$ 
E)  $V = x ( 22 - 2 x )$ 
A)  $V = x ( 22 - 2 x ) ^ { 2 }$ 
B)  $V = x + ( 22 - x ) ^ { 2 }$ 
C)  $V = x ^ { 2 } + ( 22 - 2 x )$ 
D)  $V = x ^ { 2 } ( 22 - 2 x )$ 
E)  $V = x ( 22 - 2 x )$

Question 14

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 3 } - 4$

Accepted Answer

A) $f ^ { - 1 } ( x ) = x ^ { \frac { 1 } { 3 } } + \frac { 1 } { 4 }$ 
B) $f ^ { - 1 } ( x ) = \frac { 1 } { 3 } ( x + 4 ) ^ { - \frac { 2 } { 3 } }$ 
C) $f ^ { - 1 } ( x ) = x ^ { \frac { 1 } { 3 } } + 4 ^ { \frac { 1 } { 3 } }$ 
D)  $f ^ { - 1 } ( x ) = ( x + 4 ) ^ { \frac { 1 } { 3 } }$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 3 } - 4 }$ 
A) $f ^ { - 1 } ( x ) = x ^ { \frac { 1 } { 3 } } + \frac { 1 } { 4 }$ 
B) $f ^ { - 1 } ( x ) = \frac { 1 } { 3 } ( x + 4 ) ^ { - \frac { 2 } { 3 } }$ 
C) $f ^ { - 1 } ( x ) = x ^ { \frac { 1 } { 3 } } + 4 ^ { \frac { 1 } { 3 } }$ 
D)  $f ^ { - 1 } ( x ) = ( x + 4 ) ^ { \frac { 1 } { 3 } }$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 3 } - 4 }$

$\text { Find the } y \text {-intercept of the line } x + 4 y = 8 \text {. }$

$\text { Let } f ( x ) = 14 x + 8 \text {. Then simplify the expression } \frac { f ( x ) - f ( 9 ) } { x - 9 } \text {. }$

$\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x + 5 ) \text {. }$ $\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x + 5 ) \text {. }$

$\text { A company reimburses its sales representatives } \$ 160 \text { per day for lodging and meals }$ plus 42 e per mile driven. How much does it cost the company if a sales representative drives 135 miles on a given day? Round your answer to the nearest cent.

Which function below would be most appropriate model for the given data?

$\text { Find an equation of the line through the points of intersection of } y = x ^ { 2 } \text { and }$ $y = 6 x - x ^ { 2 }$

$\text { Given } f ( x ) = \cos x \text { and } g ( x ) = \frac { \pi } { 2 } x \text {, evaluate } f ( g ( 2 ) )$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 3 } - 4$

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 1: Graphs and Models

Find the y-intercept of the line x+4y=8. \text { Find the } y \text {-intercept of the line } x + 4 y = 8 \text {. } Find the y-intercept of the line x+4y=8.

Let f(x)=14x+8. Then simplify the expression f(x)−f(9)x−9. \text { Let } f ( x ) = 14 x + 8 \text {. Then simplify the expression } \frac { f ( x ) - f ( 9 ) } { x - 9 } \text {. } Let f(x)=14x+8. Then simplify the expression x−9f(x)−f(9)​.

Use the graph of y=f(x) given below to find the graph of the function y=f(x+5). \text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x + 5 ) \text {. } Use the graph of y=f(x) given below to find the graph of the function y=f(x+5).

Which function below would be most appropriate model for the given data?

Find an equation of the line through the points of intersection of y=x2 and \text { Find an equation of the line through the points of intersection of } y = x ^ { 2 } \text { and } Find an equation of the line through the points of intersection of y=x2 and y=6x−x2y = 6 x - x ^ { 2 }y=6x−x2

Given f(x)=cos⁡x and g(x)=π2x, evaluate f(g(2))\text { Given } f ( x ) = \cos x \text { and } g ( x ) = \frac { \pi } { 2 } x \text {, evaluate } f ( g ( 2 ) ) Given f(x)=cosx and g(x)=2π​x, evaluate f(g(2))

Find f−1(x) if f(x)=x3−4\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 3 } - 4 Find f−1(x) if f(x)=x3−4

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

$\text { Find the } y \text {-intercept of the line } x + 4 y = 8 \text {. }$

$\text { Let } f ( x ) = 14 x + 8 \text {. Then simplify the expression } \frac { f ( x ) - f ( 9 ) } { x - 9 } \text {. }$

$\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x + 5 ) \text {. }$ $\text { Use the graph of } y = f ( x ) \text { given below to find the graph of the function } y = f ( x + 5 ) \text {. }$

$\text { Find an equation of the line through the points of intersection of } y = x ^ { 2 } \text { and }$ $y = 6 x - x ^ { 2 }$

$\text { Given } f ( x ) = \cos x \text { and } g ( x ) = \frac { \pi } { 2 } x \text {, evaluate } f ( g ( 2 ) )$

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 3 } - 4$