Question 1

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 2

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

Accepted Answer

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

Question 3

The function f is one-to-one. Find its inverse.
-$$( x ) = \frac { 3 } { 5 x - 2 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 3 + 2 \mathrm { y } } { 5 \mathrm { y } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 3 + 2 x } { 5 x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 2 } { 3 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 2 \mathrm { x } - 3 } { 5 \mathrm { x } }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 3 + 2 \mathrm { y } } { 5 \mathrm { y } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 3 + 2 x } { 5 x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 2 } { 3 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 2 \mathrm { x } - 3 } { 5 \mathrm { x } }$

Question 4

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2 ; \quad$ Find $\frac { r } { g }$.

Accepted Answer

A)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; \left( * , \frac { 2 } { 5 } \right) \cup \left( \frac { 2 } { 5 } , \infty \right)$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left( 0 , \frac { 2 } { 5 } \right) \cup \left( \frac { 2 } { 5 } , \infty \right)$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; ( \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 2 } { \sqrt { x } } ; [ 0 , \infty )$ 
A)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; \left( * , \frac { 2 } { 5 } \right) \cup \left( \frac { 2 } { 5 } , \infty \right)$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left( 0 , \frac { 2 } { 5 } \right) \cup \left( \frac { 2 } { 5 } , \infty \right)$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; ( \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 2 } { \sqrt { x } } ; [ 0 , \infty )$

Question 5

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = x ^ { 3 } + 4$$

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

For the given functions f and g, find the requested composite function.
-$f ( x ) = \frac { 5 } { x - 8 } , g ( x ) = \frac { 8 } { 5 x } ; \quad$ Find the function $f \circ g$.

Accepted Answer

A)  $\frac { 25 x } { 8 - 40 x }$ 
B)  $\frac { 5 x } { 8 - 40 x }$ 
C)  $\frac { 25 x } { 8 + 40 x }$ 
D)  $\frac { 8 x - 64 } { 25 x }$ 
A)  $\frac { 25 x } { 8 - 40 x }$ 
B)  $\frac { 5 x } { 8 - 40 x }$ 
C)  $\frac { 25 x } { 8 + 40 x }$ 
D)  $\frac { 8 x - 64 } { 25 x }$

Question 8

Evaluate the function at the indicated value.
-Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 5 }$

Accepted Answer

A)  $\frac { x ^ { 2 } - 3 } { x - 4 }$ 
B)  $\frac { x ^ { 2 } + 2 x + 5 } { x - 4 }$ 
C)  $\frac { x ^ { 2 } + 2 x - 3 } { x - 4 }$ 
D)  $\frac { x ^ { 2 } + 2 x - 3 } { x + 6 }$ 
A)  $\frac { x ^ { 2 } - 3 } { x - 4 }$ 
B)  $\frac { x ^ { 2 } + 2 x + 5 } { x - 4 }$ 
C)  $\frac { x ^ { 2 } + 2 x - 3 } { x - 4 }$ 
D)  $\frac { x ^ { 2 } + 2 x - 3 } { x + 6 }$

Question 9

The graph of a function f is given. Use the graph to answer the question.
-For what values of x is f(x)< 0?

Accepted Answer

A)  $( - 12,14 )$ 
B)  $( - 12 , \infty )$ 
C)  $( - \infty , - 12 )$ 
D)  $[ - 20 , - 12 ) , ( 14,20 )$ 
A)  $( - 12,14 )$ 
B)  $( - 12 , \infty )$ 
C)  $( - \infty , - 12 )$ 
D)  $[ - 20 , - 12 ) , ( 14,20 )$

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.
-$f(x)=-\sqrt{x}$

Accepted Answer

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

Question 11

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 12

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 13

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \frac { 9 + x } { x } , g ( x ) = \frac { 9 } { x - 1 }$$

Accepted Answer

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

Question 14

Find (f + g)(-3)and (f - g)(-1).

Accepted Answer

A) (f + g)(-3)= -11; (f - g)(-1)= -15 
B) (f + g)(-3)= -1; (f - g)(-1)= 3 
C) (f + g)(-3)= 29; (f - g)(-1)= 17 
D) (f + g)(-3)= -1; (f - g)(-1)= 1 
A) (f + g)(-3)= -11; (f - g)(-1)= -15 
B) (f + g)(-3)= -1; (f - g)(-1)= 3 
C) (f + g)(-3)= 29; (f - g)(-1)= 17 
D) (f + g)(-3)= -1; (f - g)(-1)= 1

Question 15

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 8 x - 6 , g ( x ) = \frac { x + 8 } { 6 }$$

Accepted Answer

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

Question 16

The function f is one-to-one. Find its inverse.
-$$f ( x ) = ( x + 7 ) ^ { 3 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 7$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 7$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 7$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 343$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 7$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 7$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 7$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 343$

Question 17

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=-(x-4)^{2}+7$

Accepted Answer

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

Question 18

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

Accepted Answer

A)  129 
B)  163 
C)  20 
D)  22 
A)  129 
B)  163 
C)  20 
D)  22

Question 19

The graph of a function f is given. Use the graph to answer the question.
-How often does the line y = -20 intersect the graph?

Accepted Answer

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

Question 20

Graph the function.
-$$f ( x ) = \sqrt [ 3 ] { x }$$

Accepted Answer

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

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

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

The function f is one-to-one. Find its inverse. - $( x ) = \frac { 3 } { 5 x - 2 }$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2 ; \quad$ Find $\frac { r } { g }$ .

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } + 4$ $Decide whether or not the functions are inverses of each other. - f ( x ) = x ^ { 3 } + 4$

For the given functions f and g, find the requested composite function. - $f ( x ) = \frac { 5 } { x - 8 } , g ( x ) = \frac { 8 } { 5 x } ; \quad$ Find the function $f \circ g$ .

Evaluate the function at the indicated value. -Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 5 }$

The graph of a function f is given. Use the graph to answer the question. -For what values of x is f(x)< 0?

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

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

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 9 + x } { x } , g ( x ) = \frac { 9 } { x - 1 }$

Find (f + g)(-3)and (f - g)(-1).

Decide whether or not the functions are inverses of each other. - $f ( x ) = 8 x - 6 , g ( x ) = \frac { x + 8 } { 6 }$

The function f is one-to-one. Find its inverse. - $f ( x ) = ( x + 7 ) ^ { 3 }$

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

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = -20 intersect the graph?

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$

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

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

Determine whether the equation defines y as a function of x. - y2=5−x2y ^ { 2 } = 5 - x ^ { 2 }y2=5−x2

The function f is one-to-one. Find its inverse. - (x)=35x−2( x ) = \frac { 3 } { 5 x - 2 }(x)=5x−23​

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - f(x)=x;g(x)=5x−2;f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2 ; \quadf(x)=x​;g(x)=5x−2; Find rg\frac { r } { g }gr​ .

Decide whether or not the functions are inverses of each other. - f(x)=x3+4f ( x ) = x ^ { 3 } + 4f(x)=x3+4

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)=−xf(x)=\sqrt{-x}f(x)=−x​

For the given functions f and g, find the requested composite function. - f(x)=5x−8,g(x)=85x;f ( x ) = \frac { 5 } { x - 8 } , g ( x ) = \frac { 8 } { 5 x } ; \quadf(x)=x−85​,g(x)=5x8​; Find the function f∘gf \circ gf∘g .

Evaluate the function at the indicated value. -Find f(x+1)f ( x + 1 )f(x+1) when f(x)=x2−4x−5f ( x ) = \frac { x ^ { 2 } - 4 } { x - 5 }f(x)=x−5x2−4​

The graph of a function f is given. Use the graph to answer the question. -For what values of x is f(x)< 0?

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)=−xf(x)=-\sqrt{x}f(x)=−x​

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

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

Decide whether or not the functions are inverses of each other. - f(x)=9+xx,g(x)=9x−1f ( x ) = \frac { 9 + x } { x } , g ( x ) = \frac { 9 } { x - 1 }f(x)=x9+x​,g(x)=x−19​

Find (f + g)(-3)and (f - g)(-1).

Decide whether or not the functions are inverses of each other. - f(x)=8x−6,g(x)=x+86f ( x ) = 8 x - 6 , g ( x ) = \frac { x + 8 } { 6 }f(x)=8x−6,g(x)=6x+8​

The function f is one-to-one. Find its inverse. - f(x)=(x+7)3f ( x ) = ( x + 7 ) ^ { 3 }f(x)=(x+7)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)=−(x−4)2+7f(x)=-(x-4)^{2}+7f(x)=−(x−4)2+7

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

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = -20 intersect the graph?

Graph the function. - f(x)=x3f ( x ) = \sqrt [ 3 ] { x }f(x)=3x​

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

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

The function f is one-to-one. Find its inverse. - $( x ) = \frac { 3 } { 5 x - 2 }$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2 ; \quad$ Find $\frac { r } { g }$ .

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } + 4$ $Decide whether or not the functions are inverses of each other. - f ( x ) = x ^ { 3 } + 4$

For the given functions f and g, find the requested composite function. - $f ( x ) = \frac { 5 } { x - 8 } , g ( x ) = \frac { 8 } { 5 x } ; \quad$ Find the function $f \circ g$ .

Evaluate the function at the indicated value. -Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 5 }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 9 + x } { x } , g ( x ) = \frac { 9 } { x - 1 }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 8 x - 6 , g ( x ) = \frac { x + 8 } { 6 }$

The function f is one-to-one. Find its inverse. - $f ( x ) = ( x + 7 ) ^ { 3 }$

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

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$