Question 1

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

Accepted Answer

A) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x + \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x - \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.$ 
D) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x + 2 & \text { if } 3 < x \leq 5 \end{array} \right.$ 
A) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x + \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x - \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.$ 
D) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x + 2 & \text { if } 3 < x \leq 5 \end{array} \right.$

Question 2

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

Accepted Answer

A)  function
 domain:{carrots, peas, squash} 
range: {Bob, Ann, Dave} 
B)  function
domain: {Bob, Ann, Dave }
range: {carrots, peas, squash} 
C)  not a function 
A)  function
 domain:{carrots, peas, squash} 
range: {Bob, Ann, Dave} 
B)  function
domain: {Bob, Ann, Dave }
range: {carrots, peas, squash} 
C)  not a function

Question 3

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=6 x^{3}$

Accepted Answer

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

Question 4

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$$\left\{ ( 2.44,3.24 ) , ( 2.444 , - 3.2 ) , \left( \frac { 7 } { 3 } , 0 \right) , ( 2.33 , - 2 ) \right\}$$

Accepted Answer

A)  function
domain: $\{ 3.24 , - 3.2,0 , - 2 \}$
range: $\left\{ 2.44,2.444 , \frac { 7 } { 3 } , 2.33 \right\}$ 
B)  function
domain: $\left\{ 2.44,2.444 , \frac { 7 } { 3 } , 2.33 \right\}$
range: $\{ 3.24 , - 3.2,0 , - 2 \}$ 
C)  not a function 
A)  function
domain: $\{ 3.24 , - 3.2,0 , - 2 \}$
range: $\left\{ 2.44,2.444 , \frac { 7 } { 3 } , 2.33 \right\}$ 
B)  function
domain: $\left\{ 2.44,2.444 , \frac { 7 } { 3 } , 2.33 \right\}$
range: $\{ 3.24 , - 3.2,0 , - 2 \}$ 
C)  not a function

Question 5

Find the value for the function.
-Find $f ( - 9 )$ when $f ( x ) = | x | - 6$.

Accepted Answer

A)  15 
B)  $- 15$ 
C)  $- 3$ 
D)  3 
A)  15 
B)  $- 15$ 
C)  $- 3$ 
D)  3

Question 6

Answer the question about the given function.
-Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x - 1$, if $x = 1$, what is $f ( x )$ ? What point is on the graph of $f$ ?

Accepted Answer

A)  $4 ; ( 1,4 )$ 
B)  $4 ; ( 4,1 )$ 
C)  $- 16 ; ( - 16,1 )$ 
D)  $- 16 ; ( 1 , - 16 )$ 
A)  $4 ; ( 1,4 )$ 
B)  $4 ; ( 4,1 )$ 
C)  $- 16 ; ( - 16,1 )$ 
D)  $- 16 ; ( 1 , - 16 )$

Question 7

Find the value for the function.
-Find $f ( 2 x )$ when $f ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }$

Accepted Answer

A)  $\sqrt { 4 x ^ { 2 } - 14 x }$ 
B)  $\sqrt { 4 x ^ { 2 } - 28 x }$ 
C)  $\sqrt { 8 x ^ { 2 } - 14 x }$ 
D)  $2 \sqrt { 2 x ^ { 2 } - 7 x }$ 
A)  $\sqrt { 4 x ^ { 2 } - 14 x }$ 
B)  $\sqrt { 4 x ^ { 2 } - 28 x }$ 
C)  $\sqrt { 8 x ^ { 2 } - 14 x }$ 
D)  $2 \sqrt { 2 x ^ { 2 } - 7 x }$

Question 8

Answer the question about the given function.
-$$\text { Given the function } f ( x ) = \frac { x ^ { 2 } - 7 } { x - 1 } \text {, is the point } ( 2 , - 3 ) \text { on the graph of } f \text { ? }$$

Accepted Answer

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

Question 9

For the function, find the average rate of change of f from 1 to x: $$\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$$
-$$f ( x ) = \frac { 6 } { x + 5 }$$

Accepted Answer

A)  $- \frac { 1 } { x + 5 }$ 
B)  $\frac { 6 } { ( x - 1 ) ( x + 5 ) }$ 
C)  $\frac { 6 } { x ( x + 5 ) }$ 
D)  $\frac { 1 } { x + 5 }$ 
A)  $- \frac { 1 } { x + 5 }$ 
B)  $\frac { 6 } { ( x - 1 ) ( x + 5 ) }$ 
C)  $\frac { 6 } { x ( x + 5 ) }$ 
D)  $\frac { 1 } { x + 5 }$

Question 10

Solve the problem.
-$$f ( x ) = \frac { 1 } { 7 x }$$

Accepted Answer

A)  $\frac { - 1 } { 7 x ( x + h ) }$ 
B)  $\frac { 1 } { 7 x }$ 
C)  0 
D)  $\frac { - 1 } { x ( x + h ) }$ 
A)  $\frac { - 1 } { 7 x ( x + h ) }$ 
B)  $\frac { 1 } { 7 x }$ 
C)  0 
D)  $\frac { - 1 } { x ( x + h ) }$

Question 11

Solve.
-The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. If a room with a perimeter of 60 feet and 6-foot walls requires 3.6 quarts of paint, find the
Amount of paint needed to cover the walls of a room with a perimeter of 45 feet and 6-foot walls.

Accepted Answer

A)  2.7 quarts 
B)  27 quarts 
C)  270 quarts 
D)  5.4 quarts 
A)  2.7 quarts 
B)  27 quarts 
C)  270 quarts 
D)  5.4 quarts

Question 12

Determine whether the equation defines y as a function of x.
-$$y = \pm \sqrt { 1 - 5 x }$$

Accepted Answer

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

Question 13

For the function, find the average rate of change of f from 1 to x: $$\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$$
-$$f ( x ) = \sqrt { x + 35 }$$

Accepted Answer

A)  $\frac { \sqrt { x + 35 } + 6 } { x - 1 }$ 
B)  $\frac { \sqrt { x + 35 } + 6 } { x + 1 }$ 
C)  $\frac { \sqrt { x + 35 } - 6 } { x + 1 }$ 
D)  $\frac { \sqrt { x + 35 } - 6 } { x - 1 }$ 
A)  $\frac { \sqrt { x + 35 } + 6 } { x - 1 }$ 
B)  $\frac { \sqrt { x + 35 } + 6 } { x + 1 }$ 
C)  $\frac { \sqrt { x + 35 } - 6 } { x + 1 }$ 
D)  $\frac { \sqrt { x + 35 } - 6 } { x - 1 }$

Question 14

Find the domain of the function.
-$$f ( x ) = \frac { x } { x ^ { 2 } + 14 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 14 \}$ 
B)  $\{ x \mid x > - 14 \}$ 
C)  $\{ x \mid x \neq 0 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq - 14 \}$ 
B)  $\{ x \mid x > - 14 \}$ 
C)  $\{ x \mid x \neq 0 \}$ 
D)  all real numbers

Question 15

Solve.
-The amount of simple interest earned on an investment over a fixed amount of time is jointly proportional to the principle invested and the interest rate. A principle investment of $1,200.00 with an interest rate of 1% earned
$60)00 in simple interest. Find the amount of simple interest earned if the principle is $1,400.00 and the interest
Rate is 5%.

Accepted Answer

A)  $70.00 
B)  $35,000.00 
C)  $350.00 
D)  $300.00 
A)  $70.00 
B)  $35,000.00 
C)  $350.00 
D)  $300.00

Question 16

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = 5 x ^ { 4 } - x ^ { 2 }$$

Accepted Answer

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

Question 17

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=x^{2}+2$

Accepted Answer

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

Question 18

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 19

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$$
Find $f \cdot g$.

Accepted Answer

A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 5 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
B)  $( f \cdot g ) ( x ) = 10 x ^ { 6 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2$; all real numbers 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 2 ;$ all real numbers 
D)  $( f \cdot g ) ( x ) = 10 x ^ { 5 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2 ; \{ x \mid x \neq 0 \}$ 
A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 5 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$; all real numbers 
B)  $( f \cdot g ) ( x ) = 10 x ^ { 6 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2$; all real numbers 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 2 ;$ all real numbers 
D)  $( f \cdot g ) ( x ) = 10 x ^ { 5 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2 ; \{ x \mid x \neq 0 \}$

Question 20

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 3 - 3 x ; g ( x ) = - 5 x + 3$$
Find $f + g$.

Accepted Answer

A)  $( f + g ) ( x ) = - 8 x + 6$; all real numbers 
B)  $( f + g ) ( x ) = - 2 x$; all real numbers 
C)  $( f + g ) ( x ) = - 5 x + 3 ; \left\{ x \mid x \neq \frac { 3 } { 5 } \right\}$ 
D)  $( f + g ) ( x ) = 2 x + 6 ; \{ x \mid x \neq 3 \}$ 
A)  $( f + g ) ( x ) = - 8 x + 6$; all real numbers 
B)  $( f + g ) ( x ) = - 2 x$; all real numbers 
C)  $( f + g ) ( x ) = - 5 x + 3 ; \left\{ x \mid x \neq \frac { 3 } { 5 } \right\}$ 
D)  $( f + g ) ( x ) = 2 x + 6 ; \{ x \mid x \neq 3 \}$

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

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

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\left\{ ( 2.44,3.24 ) , ( 2.444 , - 3.2 ) , \left( \frac { 7 } { 3 } , 0 \right) , ( 2.33 , - 2 ) \right\}$

Find the value for the function. -Find $f ( - 9 )$ when $f ( x ) = | x | - 6$ .

Answer the question about the given function. -Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x - 1$ , if $x = 1$ , what is $f ( x )$ ? What point is on the graph of $f$ ?

Find the value for the function. -Find $f ( 2 x )$ when $f ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }$

Answer the question about the given function. - $\text { Given the function } f ( x ) = \frac { x ^ { 2 } - 7 } { x - 1 } \text {, is the point } ( 2 , - 3 ) \text { on the graph of } f \text { ? }$

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \frac { 6 } { x + 5 }$

Solve the problem. - $f ( x ) = \frac { 1 } { 7 x }$

Determine whether the equation defines y as a function of x. - $y = \pm \sqrt { 1 - 5 x }$

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \sqrt { x + 35 }$

Find the domain of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 14 }$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 5 x ^ { 4 } - x ^ { 2 }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$ Find $f \cdot g$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 3 - 3 x ; g ( x ) = - 5 x + 3$ Find $f + g$ .

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

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

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)=6x3f(x)=6 x^{3}f(x)=6x3

Find the value for the function. -Find f(−9)f ( - 9 )f(−9) when f(x)=∣x∣−6f ( x ) = | x | - 6f(x)=∣x∣−6 .

Answer the question about the given function. -Given the function f(x)=−5x2+10x−1f ( x ) = - 5 x ^ { 2 } + 10 x - 1f(x)=−5x2+10x−1 , if x=1x = 1x=1 , what is f(x)f ( x )f(x) ? What point is on the graph of fff ?

Find the value for the function. -Find f(2x)f ( 2 x )f(2x) when f(x)=2x2−7xf ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }f(x)=2x2−7x​

For the function, find the average rate of change of f from 1 to x: f(x)−f(1)x−1,x≠1\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1x−1f(x)−f(1)​,x=1 - f(x)=6x+5f ( x ) = \frac { 6 } { x + 5 }f(x)=x+56​

Solve the problem. - f(x)=17xf ( x ) = \frac { 1 } { 7 x }f(x)=7x1​

Determine whether the equation defines y as a function of x. - y=±1−5xy = \pm \sqrt { 1 - 5 x }y=±1−5x​

For the function, find the average rate of change of f from 1 to x: f(x)−f(1)x−1,x≠1\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1x−1f(x)−f(1)​,x=1 - f(x)=x+35f ( x ) = \sqrt { x + 35 }f(x)=x+35​

Find the domain of the function. - f(x)=xx2+14f ( x ) = \frac { x } { x ^ { 2 } + 14 }f(x)=x2+14x​

Determine algebraically whether the function is even, odd, or neither. - f(x)=5x4−x2f ( x ) = 5 x ^ { 4 } - x ^ { 2 }f(x)=5x4−x2

Choose the one alternative that best completes the statement or answers the question. 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)=x2+2f(x)=x^{2}+2f(x)=x2+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)2f(x)=(-x)^{2}f(x)=(−x)2

For the given functions f and g, find the requested function and state its domain. - f(x)=2x3−1;g(x)=5x2+2f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2f(x)=2x3−1;g(x)=5x2+2 Find f⋅gf \cdot gf⋅g .

For the given functions f and g, find the requested function and state its domain. - f(x)=3−3x;g(x)=−5x+3f ( x ) = 3 - 3 x ; g ( x ) = - 5 x + 3f(x)=3−3x;g(x)=−5x+3 Find f+gf + gf+g .

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

Find the value for the function. -Find $f ( - 9 )$ when $f ( x ) = | x | - 6$ .

Answer the question about the given function. -Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x - 1$ , if $x = 1$ , what is $f ( x )$ ? What point is on the graph of $f$ ?

Find the value for the function. -Find $f ( 2 x )$ when $f ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }$

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \frac { 6 } { x + 5 }$

Solve the problem. - $f ( x ) = \frac { 1 } { 7 x }$

Determine whether the equation defines y as a function of x. - $y = \pm \sqrt { 1 - 5 x }$

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \sqrt { x + 35 }$

Find the domain of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 14 }$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 5 x ^ { 4 } - x ^ { 2 }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$ Find $f \cdot g$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 3 - 3 x ; g ( x ) = - 5 x + 3$ Find $f + g$ .