Question 1

Find the intersection of the given intervals.
-$( - \infty , 3 ) \cup [ - 6,13 )$

Accepted Answer

A)  $( 3,13 )$ 
B)  $( - \infty , 13 )$ 
C)  $[ - 6,3 )$ 
D)  $( - \infty , - 6 ]$ 
A)  $( 3,13 )$ 
B)  $( - \infty , 13 )$ 
C)  $[ - 6,3 )$ 
D)  $( - \infty , - 6 ]$

Question 2

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

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

Question 3

Determine whether the function is one-to-one.
-$$f ( x ) = - ( x + 6 ) ^ { 2 }$$

Accepted Answer

A) One-to-one 
B) Not one-to-one 
A) One-to-one 
B) Not one-to-one

Question 4

Solve the problem.
-An electric company has the following rate schedule for electricity usage in single-family residences:  
 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

$39.70 $49.69 \[C ( x ) = \lef

Question 5

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

Accepted Answer

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

Question 6

For the given functions f and g, find the requested composite function.
-$\mathrm { f } ( \mathrm { x } ) = 5 \mathrm { x } + 10 , \mathrm {~g} ( \mathrm { x } ) = 4 \mathrm { x } - 1 ; \quad$ Find the function $\mathrm { f } \circ \mathrm { g }$.

Accepted Answer

A)  $20 x + 15$ 
B)  $20 x + 5$ 
C)  $20 x + 9$ 
D)  $20 x + 39$ 
A)  $20 x + 15$ 
B)  $20 x + 5$ 
C)  $20 x + 9$ 
D)  $20 x + 39$

Question 7

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \sqrt [ 3 ] { x + 5 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 3 } - 5 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } - 5$ 
C)  $f ^ { - 1 } ( x ) = x ^ { 3 } + 25$ 
D)  $f ^ { - 1 } ( x ) = x ^ { 3 } - 5$ 
A)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 3 } - 5 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } - 5$ 
C)  $f ^ { - 1 } ( x ) = x ^ { 3 } + 25$ 
D)  $f ^ { - 1 } ( x ) = x ^ { 3 } - 5$

Question 8

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = x ^ { 2 } + 1$$

Accepted Answer

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

Question 9

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x } + 6$$

Accepted Answer

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

Question 10

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 11

For the given functions f and g, find the requested composite function value.
-$f ( x ) = 4 x + 2 , g ( x ) = 2 x ^ { 2 } + 3 ; \quad$ Find $( g \circ g ) ( 1 )$.

Accepted Answer

A)  75 
B)  22 
C)  53 
D)  26 
A)  75 
B)  22 
C)  53 
D)  26

Question 12

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Question 13

Use the graph to evaluate the expression.
-$$\text { Find } ( f g ) ( - 2 ) \text { and } \left( \frac { f } { g } \right) ( 4 ) \text {. }$$

Accepted Answer

A)  $( \mathrm { fg } ) ( - 2 ) = 8 ; \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 4 ) = \frac { 1 } { 12 }$ 
B)  $( f g ) ( - 2 ) = 8 ; \left( \frac { f } { g } \right) ( 4 ) = \frac { 1 } { 4 }$ 
C)  $( \mathrm { fg } ) ( - 2 ) = - 0 ; \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 4 ) = \frac { 1 } { 4 }$ 
D)  $( \mathrm { fg } ) ( - 2 ) = - 40 ; \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 4 ) = \frac { 7 } { 4 }$ 
A)  $( \mathrm { fg } ) ( - 2 ) = 8 ; \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 4 ) = \frac { 1 } { 12 }$ 
B)  $( f g ) ( - 2 ) = 8 ; \left( \frac { f } { g } \right) ( 4 ) = \frac { 1 } { 4 }$ 
C)  $( \mathrm { fg } ) ( - 2 ) = - 0 ; \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 4 ) = \frac { 1 } { 4 }$ 
D)  $( \mathrm { fg } ) ( - 2 ) = - 40 ; \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 4 ) = \frac { 7 } { 4 }$

Question 14

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \frac { 2 } { x + 4 } , g ( x ) = \frac { 4 x + 2 } { x }$$

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = 7 x - 8 ; g ( x ) = 2 x - 7 ; \quad$ Find $f - g$.

Accepted Answer

A)  $( f - g ) ( x ) = 5 x - 15 ; ( \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( f - g ) ( x ) = 5 x - 1 ; ( \infty , \infty )$ 
C)  $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = 9 \mathrm { x } - 15 ; ( \infty , 1 ) \cup ( 1 , \infty )$ 
D)  $( f - g ) ( x ) = - 5 x + 1 ; ( \infty , \infty )$ 
A)  $( f - g ) ( x ) = 5 x - 15 ; ( \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( f - g ) ( x ) = 5 x - 1 ; ( \infty , \infty )$ 
C)  $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = 9 \mathrm { x } - 15 ; ( \infty , 1 ) \cup ( 1 , \infty )$ 
D)  $( f - g ) ( x ) = - 5 x + 1 ; ( \infty , \infty )$

Question 17

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

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

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.
-$$f ( x ) = ( x + 4 ) ^ { 3 } + 7$$

Accepted Answer

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

Question 19

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

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

Question 20

Determine whether the equation defines y as a function of x.
-$$x ^ { 2 } - 5 y ^ { 2 } = 1$$

Accepted Answer

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

Find the intersection of the given intervals. - $( - \infty , 3 ) \cup [ - 6,13 )$

Use the vertical line test to determine whether the graph represents a function. -

Determine whether the function is one-to-one. - $f ( x ) = - ( x + 6 ) ^ { 2 }$

For the given functions f and g, find the requested composite function. - $\mathrm { f } ( \mathrm { x } ) = 5 \mathrm { x } + 10 , \mathrm {~g} ( \mathrm { x } ) = 4 \mathrm { x } - 1 ; \quad$ Find the function $\mathrm { f } \circ \mathrm { g }$ .

The function f is one-to-one. Find its inverse. - $f ( x ) = \sqrt [ 3 ] { x + 5 }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x } + 6$

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

For the given functions f and g, find the requested composite function value. - $f ( x ) = 4 x + 2 , g ( x ) = 2 x ^ { 2 } + 3 ; \quad$ Find $( g \circ g ) ( 1 )$ .

Use the graph to evaluate the expression. - $\text { Find } ( f g ) ( - 2 ) \text { and } \left( \frac { f } { g } \right) ( 4 ) \text {. }$ $Use the graph to evaluate the expression. - \text { Find } ( f g ) ( - 2 ) \text { and } \left( \frac { f } { g } \right) ( 4 ) \text {. }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 2 } { x + 4 } , g ( x ) = \frac { 4 x + 2 } { x }$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 7 x - 8 ; g ( x ) = 2 x - 7 ; \quad$ Find $f - g$ .

Use the horizontal line test to determine whether the function is one-to-one. -

Use the vertical line test to determine whether the graph represents a function. -

Determine whether the equation defines y as a function of x. - $x ^ { 2 } - 5 y ^ { 2 } = 1$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 3: Functions

Find the intersection of the given intervals. - (−∞,3)∪[−6,13)( - \infty , 3 ) \cup [ - 6,13 )(−∞,3)∪[−6,13)

Use the vertical line test to determine whether the graph represents a function. -

Determine whether the function is one-to-one. - f(x)=−(x+6)2f ( x ) = - ( x + 6 ) ^ { 2 }f(x)=−(x+6)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)=−x3f ( x ) = - x ^ { 3 }f(x)=−x3

The function f is one-to-one. Find its inverse. - f(x)=x+53f ( x ) = \sqrt [ 3 ] { x + 5 }f(x)=3x+5​

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+1f ( x ) = x ^ { 2 } + 1f(x)=x2+1

Decide whether or not the functions are inverses of each other. - f(x)=(x−6)2,x≥6;g(x)=x+6f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x } + 6f(x)=(x−6)2,x≥6;g(x)=x​+6

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

For the given functions f and g, find the requested composite function value. - f(x)=4x+2,g(x)=2x2+3;f ( x ) = 4 x + 2 , g ( x ) = 2 x ^ { 2 } + 3 ; \quadf(x)=4x+2,g(x)=2x2+3; Find (g∘g)(1)( g \circ g ) ( 1 )(g∘g)(1) .

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)=3xf ( x ) = \frac { 3 } { x }f(x)=x3​

Use the graph to evaluate the expression. - Find (fg)(−2) and (fg)(4). \text { Find } ( f g ) ( - 2 ) \text { and } \left( \frac { f } { g } \right) ( 4 ) \text {. } Find (fg)(−2) and (gf​)(4).

Decide whether or not the functions are inverses of each other. - f(x)=2x+4,g(x)=4x+2xf ( x ) = \frac { 2 } { x + 4 } , g ( x ) = \frac { 4 x + 2 } { x }f(x)=x+42​,g(x)=x4x+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)=2x2f(x)=2 x^{2}f(x)=2x2

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - f(x)=7x−8;g(x)=2x−7;f ( x ) = 7 x - 8 ; g ( x ) = 2 x - 7 ; \quadf(x)=7x−8;g(x)=2x−7; Find f−gf - gf−g .

Use the horizontal line test to determine whether the function is one-to-one. -

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+4)3+7f ( x ) = ( x + 4 ) ^ { 3 } + 7f(x)=(x+4)3+7

Use the vertical line test to determine whether the graph represents a function. -

Determine whether the equation defines y as a function of x. - x2−5y2=1x ^ { 2 } - 5 y ^ { 2 } = 1x2−5y2=1

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Find the intersection of the given intervals. - $( - \infty , 3 ) \cup [ - 6,13 )$

Determine whether the function is one-to-one. - $f ( x ) = - ( x + 6 ) ^ { 2 }$

The function f is one-to-one. Find its inverse. - $f ( x ) = \sqrt [ 3 ] { x + 5 }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x } + 6$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 4 x + 2 , g ( x ) = 2 x ^ { 2 } + 3 ; \quad$ Find $( g \circ g ) ( 1 )$ .

Use the graph to evaluate the expression. - $\text { Find } ( f g ) ( - 2 ) \text { and } \left( \frac { f } { g } \right) ( 4 ) \text {. }$ $Use the graph to evaluate the expression. - \text { Find } ( f g ) ( - 2 ) \text { and } \left( \frac { f } { g } \right) ( 4 ) \text {. }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 2 } { x + 4 } , g ( x ) = \frac { 4 x + 2 } { x }$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 7 x - 8 ; g ( x ) = 2 x - 7 ; \quad$ Find $f - g$ .

Determine whether the equation defines y as a function of x. - $x ^ { 2 } - 5 y ^ { 2 } = 1$