Question 1

If y varies directly as x, find a linear function which relates them.
-$y = 5$ when $x = 40$

Accepted Answer

A)  $f ( x ) = \frac { x } { 8 }$ 
B)  $f ( x ) = x + 35$ 
C)  $f ( x ) = \frac { x } { 5 }$ 
D)  $f ( x ) = 8 x$ 
A)  $f ( x ) = \frac { x } { 8 }$ 
B)  $f ( x ) = x + 35$ 
C)  $f ( x ) = \frac { x } { 5 }$ 
D)  $f ( x ) = 8 x$

Question 2

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=-x^{2}$

Accepted Answer

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

Question 3

Match the graph to the function listed whose graph most resembles the one given.
-

Accepted Answer

A)  square root function 
B)  reciprocal function 
C)  absolute value function 
D)  square function 
A)  square root function 
B)  reciprocal function 
C)  absolute value function 
D)  square function

Question 4

The graph of a function f is given. Use the graph to answer the question.
-How often does the line y = -100 intersect the graph?

Accepted Answer

A)  once 
B)  twice 
C)  three times 
D)  does not intersect 
A)  once 
B)  twice 
C)  three times 
D)  does not intersect

Question 5

Write the word or phrase that best completes each statement or answers the question.
-An electric company has the following rate schedule for electricity usage in single-family residences: $\begin{array}{llcc}
\text { Monthly service charge } & \$ 4.93\
\
\text { Per kilowatt service charge }&\
 \text {1st 300 kilowatts  } & \text { \( \$ 0.11589 / \mathrm{kW} $ }\
 \text {   Over 300 kilowatts} & \text {$ \$ 0.13321 / \mathrm{kW} $  }\

\end{array}\)

What is the charge for using 300 kilowatts in one month?
What is the charge for using 375 kilowatts in one month?
Construct a function that gives the monthly charge C for x kilowatts of electricity.

Accepted Answer

\[\begin{array} { l } 
\$ 39.70 \
\$ 49

Question 6

Determine whether the equation defines y as a function of x.
-$$y = 7 x ^ { 2 } - 2 x + 8$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 7

Choose the one alternative that best completes the statement or answers the question.
-A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11 inches by 24 inches by cutting out equal squares of side $x$ at each corner and then folding up the sides as in the figure. Express the volume $V$ of the box as a function of $x$.

Accepted Answer

A)  $V ( x ) = x ( 11 - 2 x ) ( 24 - 2 x )$ 
B)  $V ( x ) = ( 11 - x ) ( 24 - x )$ 
C)  $V ( x ) = ( 11 - 2 x ) ( 24 - 2 x )$ 
D)  $V ( x ) = x ( 11 - x ) ( 24 - x )$ 
A)  $V ( x ) = x ( 11 - 2 x ) ( 24 - 2 x )$ 
B)  $V ( x ) = ( 11 - x ) ( 24 - x )$ 
C)  $V ( x ) = ( 11 - 2 x ) ( 24 - 2 x )$ 
D)  $V ( x ) = x ( 11 - x ) ( 24 - x )$

Question 8

Write the word or phrase that best completes each statement or answers the question.
-One Internet service provider has the following rate schedule for high-speed Internet service: $$\begin{array} { l l } 
\text { Monthly service charge } & \$ 18.00 \
\text { 1st } 50 \text { hours of use } & \text { free } \
\text { Next } 50 \text { hours of use } & \$ 0.25 / \text { hour } \
\text { Over } 100 \text { hours of use } & \$ 1.00 \text { /hour }
\end{array}$$ What is the charge for 50 hours of high-speed Internet use in one month?
What is the charge for 75 hours of high-speed Internet use in one month?
What is the charge for 135 hours of high-speed Internet use in one month?

Accepted Answer

$18.00
$24

Question 9

Find the domain of the function.
-$f ( x ) = - 9 x - 2$

Accepted Answer

A)  $\{ x \mid x > 0 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x \geq 2 \}$ 
D)  all real numbers 
A)  $\{ x \mid x > 0 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x \geq 2 \}$ 
D)  all real numbers

Question 10

Choose the one alternative that best completes the statement or answers the question.
-A rectangular box with volume 433 cubic feet is built with a square base and top. The cost is $\$ 1.50$ per square foot for the top and the bottom and $\$ 2.00$ per square foot for the sides. Let $x$ represent the length of a side of the base. Express the cost the box as a function of $x$.

Accepted Answer

A)  $C ( x ) = 3 x ^ { 2 } + \frac { 3,464 } { x }$ 
B)  $C ( x ) = 4 x + \frac { 3,464 } { x ^ { 2 } }$ 
C)  $C ( x ) = 3 x ^ { 2 } + \frac { 1,732 } { x }$ 
D)  $C ( x ) = 2 x ^ { 2 } + \frac { 3,464 } { x }$ 
A)  $C ( x ) = 3 x ^ { 2 } + \frac { 3,464 } { x }$ 
B)  $C ( x ) = 4 x + \frac { 3,464 } { x ^ { 2 } }$ 
C)  $C ( x ) = 3 x ^ { 2 } + \frac { 1,732 } { x }$ 
D)  $C ( x ) = 2 x ^ { 2 } + \frac { 3,464 } { x }$

Question 11

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists.
-

Accepted Answer

A)  Absolute maximum: none; Absolute minimum: $f ( 1 ) = 2$ 
B)  Absolute maximum: $f ( 4 ) = 7$; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $\mathrm { f } ( 4 ) = 7$; Absolute minimum: none 
D)  Absolute maximum: none; Absolute minimum: none 
A)  Absolute maximum: none; Absolute minimum: $f ( 1 ) = 2$ 
B)  Absolute maximum: $f ( 4 ) = 7$; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $\mathrm { f } ( 4 ) = 7$; Absolute minimum: none 
D)  Absolute maximum: none; Absolute minimum: none

Question 12

Answer the question about the given function.
-$$\text { Given the function } f ( x ) = 5 x ^ { 2 } - 10 x - 7 \text {, is the point } ( 1 , - 12 ) \text { on the graph of } f \text { ? }$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 13

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$(-1,0)$

Accepted Answer

A)  constant 
B)  decreasing 
C)  increasing 
A)  constant 
B)  decreasing 
C)  increasing

Question 14

Solve the problem.
-A farmer has 1,600 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width $x$ of the rectangle. What is the domain of $A$ ?

Accepted Answer

A)  $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 1,600 \mathrm { x } ; \quad \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$ 
B)  $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$ 
C)  $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 800 \}$ 
D)  $A ( x ) = x ^ { 2 } + 800 x ; \{ x \mid 0 < x < 800 \}$ 
A)  $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 1,600 \mathrm { x } ; \quad \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$ 
B)  $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$ 
C)  $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 800 \}$ 
D)  $A ( x ) = x ^ { 2 } + 800 x ; \{ x \mid 0 < x < 800 \}$

Question 15

Find the function.
-Find the function that is finally graphed after the following transformations are applied to the graph of y = |x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected
Across the x-axis.

Accepted Answer

A)  y = -(3|x + 3| - 2) 
B)  y = -(3|x - 3| - 2) 
C)  y = -3|x - 3| - 2 
D)  y = 3|-x - 3| - 2 
A)  y = -(3|x + 3| - 2) 
B)  y = -(3|x - 3| - 2) 
C)  y = -3|x - 3| - 2 
D)  y = 3|-x - 3| - 2

Question 16

The graph of a function f is given. Use the graph to answer the question.
-$$\text { What is the } y \text {-intercept? }$$

Accepted Answer

A)  -8 
B)  10 
C)  7 
D)  -6 
A)  -8 
B)  10 
C)  7 
D)  -6

Question 17

Write the word or phrase that best completes each statement or answers the question.
-A right triangle has one vertex on the graph of $y = x ^ { 2 }$ at $( x , y )$, another at the origin, and the third on the (positive) $y$-axis at $( 0 , y )$. Express the area A of the triangle as a function of $x$.

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Write the word or phrase that best completes each statement or answers the question.
-Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots
(nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the
distance d between the boats as a function of the time t.

Accepted Answer

The answer of Write the word or phrase that best...

Question 19

Choose the one alternative that best completes the statement or answers the question.
-Let $P = ( x , y )$ be a point on the graph of $y = \sqrt { x }$. Express the distance $\mathrm { d }$ from $P$ to the point $( 1,0 )$ as a function of $x$

Accepted Answer

A)  $d ( x ) = x ^ { 2 } = x + 1$ 
B)  $d ( x ) = x ^ { 2 } + 2 x + 2$ 
C)  $d ( x ) = \sqrt { x ^ { 2 } + 2 x + 2 }$ 
D)  $d ( x ) = \sqrt { x ^ { 2 } - x + 1 }$ 
A)  $d ( x ) = x ^ { 2 } = x + 1$ 
B)  $d ( x ) = x ^ { 2 } + 2 x + 2$ 
C)  $d ( x ) = \sqrt { x ^ { 2 } + 2 x + 2 }$ 
D)  $d ( x ) = \sqrt { x ^ { 2 } - x + 1 }$

Question 20

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( 0,3 )$$

Accepted Answer

A)  constant 
B)  decreasing 
C)  increasing 
A)  constant 
B)  decreasing 
C)  increasing

If y varies directly as x, find a linear function which relates them. - $y = 5$ when $x = 40$

Match the graph to the function listed whose graph most resembles the one given. -

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = -100 intersect the graph?

Determine whether the equation defines y as a function of x. - $y = 7 x ^ { 2 } - 2 x + 8$

Find the domain of the function. - $f ( x ) = - 9 x - 2$

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Answer the question about the given function. - $\text { Given the function } f ( x ) = 5 x ^ { 2 } - 10 x - 7 \text {, is the point } ( 1 , - 12 ) \text { on the graph of } f \text { ? }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(-1,0)$

Solve the problem. -A farmer has 1,600 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width $x$ of the rectangle. What is the domain of $A$ ?

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of y = |x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected Across the x-axis.

The graph of a function f is given. Use the graph to answer the question. - $\text { What is the } y \text {-intercept? }$ $The graph of a function f is given. Use the graph to answer the question. - \text { What is the } y \text {-intercept? }$

Choose the one alternative that best completes the statement or answers the question. -Let $P = ( x , y )$ be a point on the graph of $y = \sqrt { x }$ . Express the distance $\mathrm { d }$ from $P$ to the point $( 1,0 )$ as a function of $x$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 0,3 )$

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 1: Functions and Their Graphs

If y varies directly as x, find a linear function which relates them. - y=5y = 5y=5 when x=40x = 40x=40

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=−x2f(x)=-x^{2}f(x)=−x2