Question 1

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = \frac { 2 x } { | x | }$$

Accepted Answer

A)  even 
B)  odd 
C)  neither 
A)  even 
B)  odd 
C)  neither

Question 2

Solve the problem.
-If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 300 milliamperes when the resistance is 2 ohms, find the current when the resistance is 12 ohms.

Accepted Answer

A)  1,800 milliamperes 
B)  1,794 milliamperes 
C)  100 milliamperes 
D)  50 milliamperes 
A)  1,800 milliamperes 
B)  1,794 milliamperes 
C)  100 milliamperes 
D)  50 milliamperes

Question 3

Graph the function.
-$$f ( x ) = | x |$$

Accepted Answer

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

Question 4

The graph of a function is given. Decide whether it is even, odd, or neither.
-

Accepted Answer

A)  even 
B)  odd 
C)  neither 
A)  even 
B)  odd 
C)  neither

Question 5

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
1 & \text { if } - 1 \leq x < 3 \
| x | & \text { if } 3 \leq x < 9 \
\sqrt { x } & \text { if } 9 \leq x \leq 11
\end{array} \right.$$

Accepted Answer

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

Question 6

Find the domain of the function.
-$$g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }$$

Accepted Answer

A)  all real numbers 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x > 81 \}$ 
D)  $\{ x \mid x \neq - 9,9 \}$ 
A)  all real numbers 
B)  $\{ x \mid x \neq 0 \}$ 
C)  $\{ x \mid x > 81 \}$ 
D)  $\{ x \mid x \neq - 9,9 \}$

Question 7

Find the average rate of change for the function between the given values.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ; \text { from } 0 \text { to } 2$$

Accepted Answer

A)  $- \frac { 1 } { 6 }$ 
B)  $- 2$ 
C)  $- 28$ 
D)  $\frac { 1 } { 2 }$ 
A)  $- \frac { 1 } { 6 }$ 
B)  $- 2$ 
C)  $- 28$ 
D)  $\frac { 1 } { 2 }$

Question 8

Write the word or phrase that best completes each statement or answers the question.
-A gas company has the following rate schedule for natural gas usage in single-family residences:
$\begin{array}{cl}
\text { Monthly service charge } & \$ 8.80 \
\text { Per therm service charge } & \
\text { 1st } 25 \text { therms } & \$ 0.6686 / \text { therm } \
\text { Over } 25 \text { therms } & \$ 0.85870 / \text { therm }
\end{array}$
 What is the charge for using 25 therms in one month?
What is the charge for using 45 therms in one month?
Construct a function that gives the monthly charge C for x therms of gas.

Accepted Answer

\[\begin{array} { l } 
\$ 25.52 \
\$ 42

Question 9

Determine whether the relation represents a function. If it is a function, state the domain and range.
-

Accepted Answer

A)  function
domain:{Ms. Lee, Mr. Bar}
range: {Bob, Ann, Dave} 
B)  function
domain: {Bob, Ann, Dave}
range: {Ms. Lee, Mr. Bar} 
C)  not a function 
A)  function
domain:{Ms. Lee, Mr. Bar}
range: {Bob, Ann, Dave} 
B)  function
domain: {Bob, Ann, Dave}
range: {Ms. Lee, Mr. Bar} 
C)  not a function

Question 10

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\frac{1}{3} \sqrt{x}$

Accepted Answer

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

Question 11

Match the function with the graph that best describes the situation.
-The height of an animal as a function of time.

Accepted Answer

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

Question 12

The graph of a piecewise-defined function is given. Write a definition for the function.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \ x & \text { if } 0 < x < 3 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 \leq x \leq 0 \ x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) 
$$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \
x & \text { if } 0 < x < 3
\end{array} \right.$$ 
D) 
$$f ( x ) = \left\{ \begin{array} { l l } 
- 2 x & \text { if } - 4 \leq x \leq 0 \
x & \text { if } 0 < x \leq 3
\end{array} \right.$$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \ x & \text { if } 0 < x < 3 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 \leq x \leq 0 \ x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) 
$$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \
x & \text { if } 0 < x < 3
\end{array} \right.$$ 
D) 
$$f ( x ) = \left\{ \begin{array} { l l } 
- 2 x & \text { if } - 4 \leq x \leq 0 \
x & \text { if } 0 < x \leq 3
\end{array} \right.$$

Question 13

The graph of a function is given. Decide whether it is even, odd, or neither.
-

Accepted Answer

A)  even 
B)  odd 
C)  neither 
A)  even 
B)  odd 
C)  neither

Question 14

Find the value for the function.
-Find $f ( x - 1 )$ when $f ( x ) = 5 x ^ { 2 } - 3 x + 1$

Accepted Answer

A)  $5 x ^ { 2 } + 2 x + 3$ 
B)  $5 x ^ { 2 } - 13 x + 9$ 
C)  $5 x ^ { 2 } - 13 x + 3$ 
D)  $- 13 x ^ { 2 } + 5 x + 9$ 
A)  $5 x ^ { 2 } + 2 x + 3$ 
B)  $5 x ^ { 2 } - 13 x + 9$ 
C)  $5 x ^ { 2 } - 13 x + 3$ 
D)  $- 13 x ^ { 2 } + 5 x + 9$

Question 15

Solve the problem.
-The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second. Find the average
Speed of the swimmer if it takes 25 seconds to finish the race.

Accepted Answer

A)  8 feet per second 
B)  7 feet per second 
C)  5 feet per second 
D)  6 feet per second 
A)  8 feet per second 
B)  7 feet per second 
C)  5 feet per second 
D)  6 feet per second

Question 16

The graph of a function f is given. Use the graph to answer the question.
-For which of the following values of x does f(x) = -16?

Accepted Answer

A)  0 
B)  12 
C)  -16 
D)  8 
A)  0 
B)  12 
C)  -16 
D)  8

Question 17

Choose the one alternative that best completes the statement or answers the question.
-From a 48-inch by 48 -inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express the volume of the box as a function of $x$.

Accepted Answer

A)  $V ( x ) = 2 x ^ { 3 } - 144 x ^ { 2 } + 48 x$ 
B)  $V ( x ) = 2 x ^ { 3 } - 144 x ^ { 2 }$ 
C)  $V ( x ) = 4 x ^ { 3 } - 192 x ^ { 2 } + 2,304 x$ 
D)  $V ( x ) = 4 x ^ { 3 } - 192 x ^ { 2 }$ 
A)  $V ( x ) = 2 x ^ { 3 } - 144 x ^ { 2 } + 48 x$ 
B)  $V ( x ) = 2 x ^ { 3 } - 144 x ^ { 2 }$ 
C)  $V ( x ) = 4 x ^ { 3 } - 192 x ^ { 2 } + 2,304 x$ 
D)  $V ( x ) = 4 x ^ { 3 } - 192 x ^ { 2 }$

Question 18

Solve the problem.
-When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 246 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new
Pressure of the gas if the volume is decreased to 41 cubic inches.

Accepted Answer

A)  78 pounds per square inch 
B)  84 pounds per square inch 
C)  70 pounds per square inch 
D)  pounds per square inch $$\frac { 41 } { 14 }$$ 
A)  78 pounds per square inch 
B)  84 pounds per square inch 
C)  70 pounds per square inch 
D)  pounds per square inch $$\frac { 41 } { 14 }$$

Question 19

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if
any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
-  2, 0)

Accepted Answer

A) 
function
domain: all real numbers
range: $ \{y \mid y \leq 9\} $
intercepts: $ (0,-4),(8,0),(0,2) $
symmetry: none 
B) 
function
domain: $ \{x \mid x \leq 9\} $
range: all real numbers
intercepts: $ (-4,0),(0,8) ,(2,0) $,
symmetry: $ y $-axis 
C) 
function
domain: all real numbers
range: $ \{y \mid y \leq 9\} $
intercepts: $ (-4,0),(0,8),(2,0) $
symmetry: none 
D) 
$\text { not a function }$ 
A) 
function
domain: all real numbers
range: $ \{y \mid y \leq 9\} $
intercepts: $ (0,-4),(8,0),(0,2) $
symmetry: none 
B) 
function
domain: $ \{x \mid x \leq 9\} $
range: all real numbers
intercepts: $ (-4,0),(0,8) ,(2,0) $,
symmetry: $ y $-axis 
C) 
function
domain: all real numbers
range: $ \{y \mid y \leq 9\} $
intercepts: $ (-4,0),(0,8),(2,0) $
symmetry: none 
D) 
$\text { not a function }$

Question 20

Solve.
-While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 28.8
Newtons when the car is moving at a speed of 20 kilometers per hour and the passenger has a mass of 80
Kilograms, find the force a passenger experiences when the car is moving at 70 kilometers per hour and the
Passenger has a mass of 90 kilograms.

Accepted Answer

A)  396.9 newtons 
B)  352.8 newtons 
C)  441 newtons 
D)  490 newtons 
A)  396.9 newtons 
B)  352.8 newtons 
C)  441 newtons 
D)  490 newtons

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 2 x } { | x | }$

Solve the problem. -If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 300 milliamperes when the resistance is 2 ohms, find the current when the resistance is 12 ohms.

Graph the function. - $f ( x ) = | x |$

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the domain of the function. - $g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }$

Find the average rate of change for the function between the given values. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ; \text { from } 0 \text { to } 2$

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Match the function with the graph that best describes the situation. -The height of an animal as a function of time.

The graph of a piecewise-defined function is given. Write a definition for the function. -

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the value for the function. -Find $f ( x - 1 )$ when $f ( x ) = 5 x ^ { 2 } - 3 x + 1$

Solve the problem. -The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second. Find the average Speed of the swimmer if it takes 25 seconds to finish the race.

The graph of a function f is given. Use the graph to answer the question. -For which of the following values of x does f(x) = -16?

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. - 2, 0)

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

Determine algebraically whether the function is even, odd, or neither. - f(x)=2x∣x∣f ( x ) = \frac { 2 x } { | x | }f(x)=∣x∣2x​

Solve the problem. -If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 300 milliamperes when the resistance is 2 ohms, find the current when the resistance is 12 ohms.

Graph the function. - f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the domain of the function. - g(x)=2xx2−81g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }g(x)=x2−812x​

Find the average rate of change for the function between the given values. - f(x)=x3+x2−8x−7; from 0 to 2f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ; \text { from } 0 \text { to } 2f(x)=x3+x2−8x−7; from 0 to 2

Determine whether the relation represents a function. If it is a function, state the domain and range. -

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)=13xf(x)=\frac{1}{3} \sqrt{x}f(x)=31​x​

Match the function with the graph that best describes the situation. -The height of an animal as a function of time.

The graph of a piecewise-defined function is given. Write a definition for the function. -

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the value for the function. -Find f(x−1)f ( x - 1 )f(x−1) when f(x)=5x2−3x+1f ( x ) = 5 x ^ { 2 } - 3 x + 1f(x)=5x2−3x+1

The graph of a function f is given. Use the graph to answer the question. -For which of the following values of x does f(x) = -16?

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. - 2, 0)

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

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 2 x } { | x | }$

Graph the function. - $f ( x ) = | x |$

Find the domain of the function. - $g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }$

Find the average rate of change for the function between the given values. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ; \text { from } 0 \text { to } 2$

Find the value for the function. -Find $f ( x - 1 )$ when $f ( x ) = 5 x ^ { 2 } - 3 x + 1$