Question 1

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = \sqrt [ 3 ] { x }$$

Accepted Answer

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

Question 2

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x + 4 & \text { if } - 9 \leq x  2
\end{array} \right.$$

Accepted Answer

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

Question 3

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
-

Accepted Answer

A)  domain: $[ 0 , \infty )$
range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$
range: $[ - 3 , \infty )$ 
C)  domain: $[ 0 , \infty )$
range: $[ 0 , \infty )$ 
D)  domain: $[ 0 , \infty )$
range: $[ - 3 , \infty )$ 
A)  domain: $[ 0 , \infty )$
range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$
range: $[ - 3 , \infty )$ 
C)  domain: $[ 0 , \infty )$
range: $[ 0 , \infty )$ 
D)  domain: $[ 0 , \infty )$
range: $[ - 3 , \infty )$

Question 4

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 5

Find the domain of the composite function f g. Write the domain in interval notation.
-$$f ( x ) = x + 3 , g ( x ) = \frac { 3 } { x + 6 }$$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( - 6 , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6 , \infty )$ 
A)  $( - \infty , - 6 ) \cup ( - 6 , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6 , \infty )$

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.
-$$f ( x ) = | 7 x |$$

Accepted Answer

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

Question 7

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 8

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = \frac { 8 x + 5 } { 2 x - 9 } ; g ( x ) = \frac { 4 x } { 2 x - 9 } ; \quad$ Find $f + g$.

Accepted Answer

A)  $( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; ( * , 0 ) \cup ( 0 , \infty )$ 
B)  $( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; \left( \infty , \frac { 9 } { 2 } \right) \cup \left( \frac { 9 } { 2 } , \infty \right)$ 
C)  $( f + g ) ( x ) = \frac { 4 x - 5 } { 2 x - 9 } ; \left( \infty , \frac { 9 } { 2 } \right) \cup \left( \frac { 9 } { 2 } , \infty \right)$ 
D)  $( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; \left( \infty , - \frac { 5 } { 12 } \right) \cup \left( - \frac { 5 } { 12 } , \infty \right)$ 
A)  $( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; ( * , 0 ) \cup ( 0 , \infty )$ 
B)  $( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; \left( \infty , \frac { 9 } { 2 } \right) \cup \left( \frac { 9 } { 2 } , \infty \right)$ 
C)  $( f + g ) ( x ) = \frac { 4 x - 5 } { 2 x - 9 } ; \left( \infty , \frac { 9 } { 2 } \right) \cup \left( \frac { 9 } { 2 } , \infty \right)$ 
D)  $( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; \left( \infty , - \frac { 5 } { 12 } \right) \cup \left( - \frac { 5 } { 12 } , \infty \right)$

Question 9

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 4 } { x }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 4 } { x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 4 \mathrm { x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 4 \mathrm { x }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { 4 } { x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 4 \mathrm { x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 4 \mathrm { x }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$

Question 10

For the given functions f and g, find the requested composite function.
-$f ( x ) = x ^ { 2 } + 6 , g ( x ) = x ^ { 2 } - 2 ; \quad$ Find the function $f \circ g$.

Accepted Answer

A)  $x ^ { 4 } - 4 x ^ { 2 } + 10$ 
B)  $x ^ { 4 } + 34$ 
C)  $x ^ { 4 } + 10$ 
D)  $x ^ { 4 } + 12 x ^ { 2 } + 34$ 
A)  $x ^ { 4 } - 4 x ^ { 2 } + 10$ 
B)  $x ^ { 4 } + 34$ 
C)  $x ^ { 4 } + 10$ 
D)  $x ^ { 4 } + 12 x ^ { 2 } + 34$

Question 11

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = 2 x + 4 ; g ( x ) = 3 x - 8 ; \quad$ Find $f \cdot g$.

Accepted Answer

A)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } - 4 x - 32 ; ( \infty , \infty )$ 
B)  $( f \cdot g ) ( x ) = 5 x ^ { 2 } - 4 x - 4 ; ( \infty , \infty )$ 
C)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 4 x - 32 ; ( \infty , - 32 ) \cup ( - 32 , \infty )$ 
D)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } - 32 ; ( \infty , - 32 ) \cup ( - 32 , \infty )$ 
A)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } - 4 x - 32 ; ( \infty , \infty )$ 
B)  $( f \cdot g ) ( x ) = 5 x ^ { 2 } - 4 x - 4 ; ( \infty , \infty )$ 
C)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } + 4 x - 32 ; ( \infty , - 32 ) \cup ( - 32 , \infty )$ 
D)  $( f \cdot g ) ( x ) = 6 x ^ { 2 } - 32 ; ( \infty , - 32 ) \cup ( - 32 , \infty )$

Question 12

Find the domain of the composite function f g. Write the domain in interval notation.
-$$f ( x ) = \sqrt { x } ; g ( x ) = 5 x + 20$$

Accepted Answer

A)  $[ - 4 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 0 , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $[ - 4 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 0 , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $( - \infty , \infty )$

Question 13

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 14

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

Accepted Answer

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

Question 15

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)= -80?

Accepted Answer

A) -80 
B) 40 
C) 60 
D) 0 
A) -80 
B) 40 
C) 60 
D) 0

Question 16

Evaluate the function at the indicated value.
-Find $f ( x + h )$ when $f ( x ) = 3 x ^ { 2 } + 5 x + 2$

Accepted Answer

A)  $3 x ^ { 2 } + 3 h ^ { 2 } + 5 x + 5 h + 2$ 
B)  $3 \mathrm { x } ^ { 2 } + 3 \mathrm {~h} ^ { 2 } + 11 \mathrm { x } + 11 \mathrm {~h} + 2$ 
C)  $3 x ^ { 2 } + 3 x h + 3 h ^ { 2 } + 5 x + 5 h + 2$ 
D)  $3 x ^ { 2 } + 6 x h + 3 h ^ { 2 } + 5 x + 5 h + 2$ 
A)  $3 x ^ { 2 } + 3 h ^ { 2 } + 5 x + 5 h + 2$ 
B)  $3 \mathrm { x } ^ { 2 } + 3 \mathrm {~h} ^ { 2 } + 11 \mathrm { x } + 11 \mathrm {~h} + 2$ 
C)  $3 x ^ { 2 } + 3 x h + 3 h ^ { 2 } + 5 x + 5 h + 2$ 
D)  $3 x ^ { 2 } + 6 x h + 3 h ^ { 2 } + 5 x + 5 h + 2$

Question 17

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
-$$f ( t ) = t ^ { 2 } + 2$$

Accepted Answer

A)  polynomial function; $( \infty , \infty )$ 
B)  polynomial function; $( - 2 , \infty )$ 
C)  polynomial function; $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  polynomial function; $[ - 2 , \infty )$ 
A)  polynomial function; $( \infty , \infty )$ 
B)  polynomial function; $( - 2 , \infty )$ 
C)  polynomial function; $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  polynomial function; $[ - 2 , \infty )$

Question 18

The function f is one-to-one. Find its inverse.
-$$f ( x ) = x ^ { 3 } + 1$$

Accepted Answer

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

Question 19

Graph the function.
-$$f ( x ) = \frac { 1 } { x }$$

Accepted Answer

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

Question 20

Determine whether the function is one-to-one.
-$$f ( x ) = x ^ { 3 } - 3$$

Accepted Answer

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

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \sqrt [ 3 ] { x }$

Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

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

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = x + 3 , g ( x ) = \frac { 3 } { x + 6 }$

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

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 function and state its domain. Write the domain in interval notation. - $f ( x ) = \frac { 8 x + 5 } { 2 x - 9 } ; g ( x ) = \frac { 4 x } { 2 x - 9 } ; \quad$ Find $f + g$ .

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 4 } { x }$

For the given functions f and g, find the requested composite function. - $f ( x ) = x ^ { 2 } + 6 , g ( x ) = x ^ { 2 } - 2 ; \quad$ Find the function $f \circ g$ .

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 2 x + 4 ; g ( x ) = 3 x - 8 ; \quad$ Find $f \cdot g$ .

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x + 20$

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)= -80?

Evaluate the function at the indicated value. -Find $f ( x + h )$ when $f ( x ) = 3 x ^ { 2 } + 5 x + 2$

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - $f ( t ) = t ^ { 2 } + 2$

The function f is one-to-one. Find its inverse. - $f ( x ) = x ^ { 3 } + 1$

Graph the function. - $f ( x ) = \frac { 1 } { x }$ $Graph the function. - f ( x ) = \frac { 1 } { x }$

Determine whether the function is one-to-one. - $f ( x ) = x ^ { 3 } - 3$

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

Determine algebraically whether the function is even, odd, or neither. - f(x)=x3f ( x ) = \sqrt [ 3 ] { x }f(x)=3x​

Graph the function. - f(x)={x+4 if −9≤x<2−4 if x=2−x+4 if x>2f ( x ) = \left\{ \begin{array} { l l } x + 4 & \text { if } - 9 \leq x < 2 \\- 4 & \text { if } x = 2 \\- x + 4 & \text { if } x > 2\end{array} \right.f(x)=⎩⎨⎧​x+4−4−x+4​ if −9≤x<2 if x=2 if x>2​

Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

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

Find the domain of the composite function f g. Write the domain in interval notation. - f(x)=x+3,g(x)=3x+6f ( x ) = x + 3 , g ( x ) = \frac { 3 } { x + 6 }f(x)=x+3,g(x)=x+63​

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)=∣7x∣f ( x ) = | 7 x |f(x)=∣7x∣

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 function and state its domain. Write the domain in interval notation. - f(x)=8x+52x−9;g(x)=4x2x−9;f ( x ) = \frac { 8 x + 5 } { 2 x - 9 } ; g ( x ) = \frac { 4 x } { 2 x - 9 } ; \quadf(x)=2x−98x+5​;g(x)=2x−94x​; Find f+gf + gf+g .

The function f is one-to-one. Find its inverse. - f(x)=4xf ( x ) = \frac { 4 } { x }f(x)=x4​

For the given functions f and g, find the requested composite function. - f(x)=x2+6,g(x)=x2−2;f ( x ) = x ^ { 2 } + 6 , g ( x ) = x ^ { 2 } - 2 ; \quadf(x)=x2+6,g(x)=x2−2; Find the function f∘gf \circ gf∘g .

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - f(x)=2x+4;g(x)=3x−8;f ( x ) = 2 x + 4 ; g ( x ) = 3 x - 8 ; \quadf(x)=2x+4;g(x)=3x−8; Find f⋅gf \cdot gf⋅g .

Find the domain of the composite function f g. Write the domain in interval notation. - f(x)=x;g(x)=5x+20f ( x ) = \sqrt { x } ; g ( x ) = 5 x + 20f(x)=x​;g(x)=5x+20

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

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)=∣13x∣f(x)=\left|\frac{1}{3} x\right|f(x)=​31​x​

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)= -80?

Evaluate the function at the indicated value. -Find f(x+h)f ( x + h )f(x+h) when f(x)=3x2+5x+2f ( x ) = 3 x ^ { 2 } + 5 x + 2f(x)=3x2+5x+2

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - f(t)=t2+2f ( t ) = t ^ { 2 } + 2f(t)=t2+2

The function f is one-to-one. Find its inverse. - f(x)=x3+1f ( x ) = x ^ { 3 } + 1f(x)=x3+1

Graph the function. - f(x)=1xf ( x ) = \frac { 1 } { x }f(x)=x1​

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

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 algebraically whether the function is even, odd, or neither. - $f ( x ) = \sqrt [ 3 ] { x }$

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = x + 3 , g ( x ) = \frac { 3 } { x + 6 }$

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

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = \frac { 8 x + 5 } { 2 x - 9 } ; g ( x ) = \frac { 4 x } { 2 x - 9 } ; \quad$ Find $f + g$ .

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 4 } { x }$

For the given functions f and g, find the requested composite function. - $f ( x ) = x ^ { 2 } + 6 , g ( x ) = x ^ { 2 } - 2 ; \quad$ Find the function $f \circ g$ .

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 2 x + 4 ; g ( x ) = 3 x - 8 ; \quad$ Find $f \cdot g$ .

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x + 20$

Evaluate the function at the indicated value. -Find $f ( x + h )$ when $f ( x ) = 3 x ^ { 2 } + 5 x + 2$

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - $f ( t ) = t ^ { 2 } + 2$

The function f is one-to-one. Find its inverse. - $f ( x ) = x ^ { 3 } + 1$

Graph the function. - $f ( x ) = \frac { 1 } { x }$ $Graph the function. - f ( x ) = \frac { 1 } { x }$

Determine whether the function is one-to-one. - $f ( x ) = x ^ { 3 } - 3$