Question 1

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

Accepted Answer

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

Question 2

For the given functions f and g, find the requested composite function value.
-$$f ( x ) = 4 x + 6 , g ( x ) = 2 x ^ { 2 } + 1 ; \quad \text { Find } ( f \circ f ) ( 4 )$$

Accepted Answer

A) 138 
B) 94 
C) 969 
D) 2179 
A) 138 
B) 94 
C) 969 
D) 2179 B

Question 3

Find the rule that defines each piecewise-defined function.
-

Accepted Answer

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

Question 4

Determine whether the function is one-to-one.
-$$h ( x ) = \frac { 1 } { 6 } x - \frac { 7 } { 6 }$$

Accepted Answer

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

Question 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?

Accepted Answer

A)  $[ - 5 , - 3 ) , ( 3.5,5 )$ 
B)  $( - 3,3.5 )$ 
C)  $( - \infty - 3 )$ 
D)  $( - 3 , \infty )$ 
A)  $[ - 5 , - 3 ) , ( 3.5,5 )$ 
B)  $( - 3,3.5 )$ 
C)  $( - \infty - 3 )$ 
D)  $( - 3 , \infty )$

Question 6

Determine the domain of f.
-$f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \neq 0 \ 5 & \text { if } x = 0 \end{array} \right.$

Accepted Answer

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

Question 7

Evaluate the function at the indicated value.
-Find $f ( 6 )$ when $f ( x ) = \sqrt { x ^ { 2 } + 7 x }$.

Accepted Answer

A)  $\sqrt { 78 }$ 
B)  $2 \sqrt { 14 }$ 
C)  $\sqrt { 85 }$ 
D)  $\sqrt { 43 }$ 
A)  $\sqrt { 78 }$ 
B)  $2 \sqrt { 14 }$ 
C)  $\sqrt { 85 }$ 
D)  $\sqrt { 43 }$

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.
-$f(x)=\frac{1}{5}|x|$

Accepted Answer

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

Question 9

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = 3 x ^ { 4 } - x ^ { 2 }$$

Accepted Answer

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

Question 10

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 11

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
-$$h ( t ) = \frac { t - 4 } { t ^ { 3 } - 9 t }$$

Accepted Answer

A)  rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  rational function; $( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  rational function; $( \alpha , \infty )$ 
D)  rational function; $( \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0,3 ) \cup ( 3 , \infty )$ 
A)  rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  rational function; $( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  rational function; $( \alpha , \infty )$ 
D)  rational function; $( \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0,3 ) \cup ( 3 , \infty )$

Question 12

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation.
-$$h ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 8 }$$

Accepted Answer

A)  rational function; $( \infty , \infty )$ 
B)  rational function; $( - 8 , \infty )$ 
C)  rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  rational function; $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
A)  rational function; $( \infty , \infty )$ 
B)  rational function; $( - 8 , \infty )$ 
C)  rational function; $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  rational function; $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question 13

Solve the problem.
-A gas company has the following rate schedule for natural gas usage in single-family residences:  
 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

$25.52 $42.69 \[C ( x ) = \lef

Question 14

Use the accompanying graph of y = f(x)to sketch the graph of the indicated equation.
-$y=-2 f(x+3)+2$

Accepted Answer

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

Question 15

Evaluate.
-Find (f - g)(-2)when f(x)= 5x2 + 1 and g(x)= x + 4.

Accepted Answer

A) 19 
B) 15 
C) -19 
D) 27 
A) 19 
B) 15 
C) -19 
D) 27

Question 16

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=(x-4)^{3}$

Accepted Answer

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

Question 17

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 18

Evaluate the function at the indicated value.
-Find f(x - 1)when f(x)= 4x2 + 3x + 1.

Accepted Answer

A)  $4 x ^ { 2 } - 5 x + 8$ 
B)  $- 5 x ^ { 2 } + 4 x + 2$ 
C)  $4 x ^ { 2 } - 5 x + 2$ 
D)  $4 x ^ { 2 } + 7 x + 8$ 
A)  $4 x ^ { 2 } - 5 x + 8$ 
B)  $- 5 x ^ { 2 } + 4 x + 2$ 
C)  $4 x ^ { 2 } - 5 x + 2$ 
D)  $4 x ^ { 2 } + 7 x + 8$

Question 19

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

Accepted Answer

A) not a function 
B) function 
C) function domain: {cat, dog} domain: {Alice, Brad, Carl}
Range: {Alice, Brad, Carl} range: {cat, dog} 
A) not a function 
B) function 
C) function domain: {cat, dog} domain: {Alice, Brad, Carl}
Range: {Alice, Brad, Carl} range: {cat, dog}

Question 20

Graph the function.
-f(x)= x

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

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

For the given functions f and g, find the requested composite function value. - $f ( x ) = 4 x + 6 , g ( x ) = 2 x ^ { 2 } + 1 ; \quad \text { Find } ( f \circ f ) ( 4 )$

Find the rule that defines each piecewise-defined function. -

Determine whether the function is one-to-one. - $h ( x ) = \frac { 1 } { 6 } x - \frac { 7 } { 6 }$

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

Determine the domain of f. - $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \neq 0 \\ 5 & \text { if } x = 0 \end{array} \right.$

Evaluate the function at the indicated value. -Find $f ( 6 )$ when $f ( x ) = \sqrt { x ^ { 2 } + 7 x }$ .

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 3 x ^ { 4 } - x ^ { 2 }$

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

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - $h ( t ) = \frac { t - 4 } { t ^ { 3 } - 9 t }$

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - $h ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 8 }$

Solve the problem. -A gas company has the following rate schedule for natural gas usage in single-family residences: 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.

Use the accompanying graph of y = f(x)to sketch the graph of the indicated equation. - $y=-2 f(x+3)+2$

Evaluate. -Find (f - g)(-2)when f(x)= 5x2 + 1 and g(x)= x + 4.

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

Evaluate the function at the indicated value. -Find f(x - 1)when f(x)= 4x2 + 3x + 1.

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

Graph the function. -f(x)= 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

Determine whether the function is one-to-one. - f(x)=x2+2f ( x ) = x ^ { 2 } + 2f(x)=x2+2

For the given functions f and g, find the requested composite function value. - f(x)=4x+6,g(x)=2x2+1; Find (f∘f)(4)f ( x ) = 4 x + 6 , g ( x ) = 2 x ^ { 2 } + 1 ; \quad \text { Find } ( f \circ f ) ( 4 )f(x)=4x+6,g(x)=2x2+1; Find (f∘f)(4)

Find the rule that defines each piecewise-defined function. -

Determine whether the function is one-to-one. - h(x)=16x−76h ( x ) = \frac { 1 } { 6 } x - \frac { 7 } { 6 }h(x)=61​x−67​

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

Determine the domain of f. - f(x)={2x if x≠05 if x=0f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \neq 0 \\ 5 & \text { if } x = 0 \end{array} \right.f(x)={2x5​ if x=0 if x=0​

Evaluate the function at the indicated value. -Find f(6)f ( 6 )f(6) when f(x)=x2+7xf ( x ) = \sqrt { x ^ { 2 } + 7 x }f(x)=x2+7x​ .

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)=15∣x∣f(x)=\frac{1}{5}|x|f(x)=51​∣x∣

Determine algebraically whether the function is even, odd, or neither. - f(x)=3x4−x2f ( x ) = 3 x ^ { 4 } - x ^ { 2 }f(x)=3x4−x2

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

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - h(t)=t−4t3−9th ( t ) = \frac { t - 4 } { t ^ { 3 } - 9 t }h(t)=t3−9tt−4​

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - h(x)=x2x2+8h ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 8 }h(x)=x2+8x2​

Solve the problem. -A gas company has the following rate schedule for natural gas usage in single-family residences: 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.

Use the accompanying graph of y = f(x)to sketch the graph of the indicated equation. - y=−2f(x+3)+2y=-2 f(x+3)+2y=−2f(x+3)+2

Evaluate. -Find (f - g)(-2)when f(x)= 5x2 + 1 and g(x)= x + 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)=(x−4)3f(x)=(x-4)^{3}f(x)=(x−4)3

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

Evaluate the function at the indicated value. -Find f(x - 1)when f(x)= 4x2 + 3x + 1.

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

Graph the function. -f(x)= 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

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

For the given functions f and g, find the requested composite function value. - $f ( x ) = 4 x + 6 , g ( x ) = 2 x ^ { 2 } + 1 ; \quad \text { Find } ( f \circ f ) ( 4 )$

Determine whether the function is one-to-one. - $h ( x ) = \frac { 1 } { 6 } x - \frac { 7 } { 6 }$

Determine the domain of f. - $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \neq 0 \\ 5 & \text { if } x = 0 \end{array} \right.$

Evaluate the function at the indicated value. -Find $f ( 6 )$ when $f ( x ) = \sqrt { x ^ { 2 } + 7 x }$ .

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 3 x ^ { 4 } - x ^ { 2 }$

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - $h ( t ) = \frac { t - 4 } { t ^ { 3 } - 9 t }$

Classify the function as a polynomial function, rational function, or root function, and then find the domain. Write the domain in interval notation. - $h ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 8 }$

Use the accompanying graph of y = f(x)to sketch the graph of the indicated equation. - $y=-2 f(x+3)+2$