Question 1

Which of the following is the correct graph of the function   ?

Accepted Answer

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

Question 2

Determine all asymptotes for the graph of the given function. Match your result to the correct answer below.

Accepted Answer

A)  Vertical : x = -8; Oblique: y = 5x. 
B)  Vertical : x = 8; Horizontal: x-axis. 
C)  Vertical : x = 8. 
D)  Vertical : x = 8; Oblique: y = 5x + 40. 
A)  Vertical : x = -8; Oblique: y = 5x. 
B)  Vertical : x = 8; Horizontal: x-axis. 
C)  Vertical : x = 8. 
D)  Vertical : x = 8; Oblique: y = 5x + 40. D

Question 3

Determine whether the relation |6x| = |-7y| is a function.

Accepted Answer

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

Question 4

Which piecewise function is represented by the graph?

Accepted Answer

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

Question 5

Let f(x) = x2 - 2x + 3, g(x) = -2x + 2, and h(x) = |x - 3|. Which of the following is the correct evaluation of   ?

Accepted Answer

A)    
B)    
C)  2 
D)    
A)    
B)    
C)  2 
D)

Question 6

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x2 + 7x + 12

Accepted Answer

A)  Crosses at (-4, 0) and (3, 0) 
B)  Crosses at (4, 0) and (-3, 0) 
C)  Crosses at (4, 0) and (3, 0) 
D)  Crosses at (-4, 0) and (-3, 0) 
A)  Crosses at (-4, 0) and (3, 0) 
B)  Crosses at (4, 0) and (-3, 0) 
C)  Crosses at (4, 0) and (3, 0) 
D)  Crosses at (-4, 0) and (-3, 0)

Question 7

Use the vertical line test to determine which of the following graphs is not the graph of a function.

Accepted Answer

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

Question 8

Which of the following choices correctly shows the graphs of   and its inverse?

Accepted Answer

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

Question 9

How are the graphs of f(x) = x2 and g(x) = x2 + 6 related?

Accepted Answer

A)  The graph of g(x) is the same as that of f(x), but translated upward by 6 units. 
B)  The graph of g(x) is the same as that of f(x), but translated downward by 6 units. 
C)  The graph of g(x) is the same as that of f(x), but translated 6 units to the right. 
D)  The graph of g(x) is the same as that of f(x), but translated 6 units to the left. 
A)  The graph of g(x) is the same as that of f(x), but translated upward by 6 units. 
B)  The graph of g(x) is the same as that of f(x), but translated downward by 6 units. 
C)  The graph of g(x) is the same as that of f(x), but translated 6 units to the right. 
D)  The graph of g(x) is the same as that of f(x), but translated 6 units to the left.

Question 10

Which choice below is the correct graph of   ?

Accepted Answer

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

Question 11

Which of the following gives the correct domain and range of the relation {(-6, 1), (0, 1)}?

Accepted Answer

A)  Domain = {-6, 0, 1}, range = {1} 
B)  Domain = {1}, range = {-6, 0} 
C)  Domain =
  , range = {1} 
D)  Domain = {-6, 0}, range = {1} 
A)  Domain = {-6, 0, 1}, range = {1} 
B)  Domain = {1}, range = {-6, 0} 
C)  Domain =
  , range = {1} 
D)  Domain = {-6, 0}, range = {1}

Question 12

Determine whether the table expresses the second variable as a function of the first variable.

Accepted Answer

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

Question 13

Determine whether the given function is invertible. If it is invertible, then find its inverse. Match your results to the correct answer below. {(-10,-13),(-8,-2),(1,-7)}

Accepted Answer

A)  No 
B)  Yes ; {(-13,-10),(-2,-8),(-7,1)} 
C)  Yes ; {(-10,13),(-8,2),(1,7)} 
D)  Yes ; {(10,13),(8,2),(-1,7)} 
A)  No 
B)  Yes ; {(-13,-10),(-2,-8),(-7,1)} 
C)  Yes ; {(-10,13),(-8,2),(1,7)} 
D)  Yes ; {(10,13),(8,2),(-1,7)}

Question 14

Which choice below is the correct graph of   ?

Accepted Answer

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

Question 15

How are the graphs of f(x) = (x + 10)2 and g(x) = -(x + 10)2 related?

Accepted Answer

A)  The graph of g(x) is the same as that of f(x), but reflected about the x-axis. 
B)  The graph of g(x) is the same as that of f(x), but translated upward by 10 units. 
C)  The graph of g(x) is the same as that of f(x), but translated 10 units to the left. 
D)  The graph of g(x) is the same as that of f(x), but translated 10 units to the right. 
A)  The graph of g(x) is the same as that of f(x), but reflected about the x-axis. 
B)  The graph of g(x) is the same as that of f(x), but translated upward by 10 units. 
C)  The graph of g(x) is the same as that of f(x), but translated 10 units to the left. 
D)  The graph of g(x) is the same as that of f(x), but translated 10 units to the right.

Question 16

How are the graphs of   and   related?

Accepted Answer

A)  The graph of g(x) is the same as that of f(x), but stretched along the y-axis by a factor of 9. 
B)  The graph of g(x) is the same as that of f(x), but translated downward by 9 units. 
C)  The graph of g(x) is the same as that of f(x), but shrunk along the y-axis by a factor of 9. 
D)  The graph of g(x) is the same as that of f(x), but translated upward by 9 units. 
A)  The graph of g(x) is the same as that of f(x), but stretched along the y-axis by a factor of 9. 
B)  The graph of g(x) is the same as that of f(x), but translated downward by 9 units. 
C)  The graph of g(x) is the same as that of f(x), but shrunk along the y-axis by a factor of 9. 
D)  The graph of g(x) is the same as that of f(x), but translated upward by 9 units.

Question 17

Find the domain of the given rational function. Match your result to the correct answer below.

Accepted Answer

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

Question 18

Determine   for   . Match your result to the correct answer below.

Accepted Answer

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

Question 19

Let f(x) = 2x + 3 and g(x) = x2 - 6x. Find   and match your result to the correct answer below.

Accepted Answer

A)  2x2 - 12 
B)  2x2 + 12x + 3 
C)  2x2 - 12x + 3 
D)  2x3 - 9x2 + 3x 
A)  2x2 - 12 
B)  2x2 + 12x + 3 
C)  2x2 - 12x + 3 
D)  2x3 - 9x2 + 3x

Question 20

Determine whether f(x) = 5x and g(x) = 0.2x are inverses of each other.

Accepted Answer

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

Exam 11: Section 1: Functions

Which of the following is the correct graph of the function ?

Determine all asymptotes for the graph of the given function. Match your result to the correct answer below.

Determine whether the relation |6x| = |-7y| is a function.

Which piecewise function is represented by the graph?

Let f(x) = x2 - 2x + 3, g(x) = -2x + 2, and h(x) = |x - 3|. Which of the following is the correct evaluation of ?

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x2 + 7x + 12

Use the vertical line test to determine which of the following graphs is not the graph of a function.

Which of the following choices correctly shows the graphs of and its inverse?

How are the graphs of f(x) = x2 and g(x) = x2 + 6 related?

Which choice below is the correct graph of ?

Which of the following gives the correct domain and range of the relation {(-6, 1), (0, 1)}?

Determine whether the table expresses the second variable as a function of the first variable.

Determine whether the given function is invertible. If it is invertible, then find its inverse. Match your results to the correct answer below. {(-10,-13),(-8,-2),(1,-7)}

Which choice below is the correct graph of ?

How are the graphs of f(x) = (x + 10)2 and g(x) = -(x + 10)2 related?

How are the graphs of and related?

Find the domain of the given rational function. Match your result to the correct answer below.

Determine for . Match your result to the correct answer below.

Let f(x) = 2x + 3 and g(x) = x2 - 6x. Find and match your result to the correct answer below.

Determine whether f(x) = 5x and g(x) = 0.2x are inverses of each other.

Section 1: Real Numbers and Their Properties

Section 2: Real Numbers and Their Properties

Section 1: Linear Equations and Inequalities in One Variable

Section 2: Linear Equations and Inequalities in One Variable

Section 1: Linear Equations and Inequalities in Two Variables

Section 2: Linear Equations and Inequalities in Two Variables

Section 1: Exponents and Polynomials

Section 2: Exponents and Polynomials

Section 1: Factoring

Section 2: Factoring

Section 1: Rational Expressions

Section 2: Rational Expressions

Section 1: Systems of Linear Equations

Section 2: Systems of Linear Equations

Section 1: More on Inequalities

Section 2: More on Inequalities

Section 1: Radicals and Rational Exponents

Section 2: Radicals and Rational Exponents

Section 1: Quadratic Equations and Inequalities

Section 2: Quadratic Equations and Inequalities

Section 2: Functions

Section 1: Exponential and Logarithmic Functions

Section 2: Exponential and Logarithmic Functions

Section 1: Nonlinear Systems and the Conic Sections

Section 2: Nonlinear Systems and the Conic Sections

Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Section 2: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Mathematical Problem Set

Algebraic Equations and Problem Solving

Algebra and Math Problems

Algebraic Equation Practice

Filters

Let f(x) = x² - 2x + 3, g(x) = -2x + 2, and h(x) = |x - 3|. Which of the following is the correct evaluation of ?

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x² + 7x + 12

How are the graphs of f(x) = x² and g(x) = x² + 6 related?

How are the graphs of f(x) = (x + 10)² and g(x) = -(x + 10)² related?

Let f(x) = 2x + 3 and g(x) = x² - 6x. Find and match your result to the correct answer below.