Question 1

Suppose that f and g are the functions defined by the tables below. What is the range of g?

Accepted Answer

A)  {8, 9, 10, 11} 
B)  {9, 10, 11, 12} 
C)  {10, 11, 12, 13} 
D)  {7, 8, 9, 10} 
A)  {8, 9, 10, 11} 
B)  {9, 10, 11, 12} 
C)  {10, 11, 12, 13} 
D)  {7, 8, 9, 10}

Question 2

Suppose h(x) = -11 + x2, where the domain of h is the set of positive numbers. Find a formula for h-1.

Accepted Answer

Question 3

Find the domain of 
   
 .

Accepted Answer

The answer of Find the domain of 
  ...

Question 4

Assume that 
   for each real number x different of 0. Evaluate and simplify the expression
   
 .

Accepted Answer

The answer of Assume that 
   for each...

Question 5

Let f(x) = x2 and g(x) = x2 + 2x + 2. Which of the following alternatives best describes the relationship between the graph of f and g?

Accepted Answer

A)  The graph of g is obtained by shifting the graph of f up one unit 
B)  The graph of g is obtained by shifting the graph of f up one unit and shifting right one unit 
C)  The graph of g is obtained by shifting the graph of f down one unit and shifting it right one unit 
D)  The graph of g is obtained by shifting the graph of f up one unit and shifting left one unit 
A)  The graph of g is obtained by shifting the graph of f up one unit 
B)  The graph of g is obtained by shifting the graph of f up one unit and shifting right one unit 
C)  The graph of g is obtained by shifting the graph of f down one unit and shifting it right one unit 
D)  The graph of g is obtained by shifting the graph of f up one unit and shifting left one unit

Question 6

Choose the composite of functions that would create the graph:

Accepted Answer

A) 
  For  And   
B) 
  For  And   
C) 
  For  And   
D) 
  For  And   
A) 
  For  And   
B) 
  For  And   
C) 
  For  And   
D) 
  For  And

Question 7

Suppose f(x) = 5x3 + x. Which of the following alternatives equals f -1(630)?

Accepted Answer

A)  5 
B) 
  
C)  6 
D) 
  
A)  5 
B) 
  
C)  6 
D)

Question 8

Choose the composite of functions that would create the graph:

Accepted Answer

A) 
  For  And   
B) 
  For  And   
C) 
  For  And   
D)   For  And   
A) 
  For  And   
B) 
  For  And   
C) 
  For  And   
D)   For  And

Question 9

Suppose that f is the function defined by the table below. What is the domain of f -1?

Accepted Answer

A)  {8, 9, 10, 11} 
B) 
  
C)  {10, 11, 12, 13} 
D)  {8, 10, 12, 14} 
A)  {8, 9, 10, 11} 
B) 
  
C)  {10, 11, 12, 13} 
D)  {8, 10, 12, 14}

Question 10

Which of the following functions has domain   ?

Accepted Answer

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

Question 11

Suppose that g is the function defined by the table below. What is the range of g -1?

Accepted Answer

Question 12

Give the coordinates of the point  Using the figure below.

Accepted Answer

A)  (0, -1) 
B)  (1, -1) 
C)  (-1, 1) 
D)  (1, 0) 
A)  (0, -1) 
B)  (1, -1) 
C)  (-1, 1) 
D)  (1, 0)

Question 13

Assume that f is a function whose domain is the interval 
   
, whose range is the interval
   
, and whose graph is the figure below. For g(x) = f(x + 2),

A) find the domain of g.
B) find the range of g.
C) sketch the graph of g.

Accepted Answer

Part A:
 @#IMG-DLM&

Question 14

Assume that  For each real number x. Evaluate and simplify the following expression.

Accepted Answer

A)  3 
B)  9 
C)  0 
D) 
   
A)  3 
B)  9 
C)  0 
D)

Question 15

Suppose f(x) = -x - 16. Evaluate f -1(-11).

Accepted Answer

A)  16 
B)  14 
C)  -5 
D)  15 
A)  16 
B)  14 
C)  -5 
D)  15

Question 16

Assume that f is the function with domain [-3, 3] whose graph is shown below. Estimate a number b such that f(b) + f(-b) = 2.

Accepted Answer

A)  1.5 
B)  1 
C)  2 
D)  0 
A)  1.5 
B)  1 
C)  2 
D)  0

Question 17

Choose the composite of functions that would create the graph:

Accepted Answer

A) 
  For  And   
B) 
  For  And   
C) 
  For  And   
D) 
  For  And   
A) 
  For  And   
B) 
  For  And   
C) 
  For  And   
D) 
  For  And

Question 18

Suppose 
    . If   , then find a function g such that
   
 .

Accepted Answer

The answer of Suppose 
    . If...

Question 19

Suppose   
 . Evaluate f -1(4).

Accepted Answer

A)  4 
B)  5 
C)  3 
D)  -4 
A)  4 
B)  5 
C)  3 
D)  -4

Question 20

Choose the table that represents a function.

Accepted Answer

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

Suppose that f and g are the functions defined by the tables below. What is the range of g?

Suppose h(x) = -11 + x², where the domain of h is the set of positive numbers. Find a formula for h^-¹.

Find the domain of .

Assume that for each real number x different of 0. Evaluate and simplify the expression .

Let f(x) = x² and g(x) = x² + 2x + 2. Which of the following alternatives best describes the relationship between the graph of f and g?

Choose the composite of functions that would create the graph:

Suppose f(x) = 5x³ + x. Which of the following alternatives equals f^-¹(630)?

Choose the composite of functions that would create the graph:

Suppose that f is the function defined by the table below. What is the domain of f ^-¹?

Which of the following functions has domain ?

Suppose that g is the function defined by the table below. What is the range of g ^-¹?

Give the coordinates of the point Using the figure below.

Assume that f is a function whose domain is the interval , whose range is the interval , and whose graph is the figure below. For g(x) = f(x + 2), A) find the domain of g. B) find the range of g. C) sketch the graph of g.

Assume that For each real number x. Evaluate and simplify the following expression.

Suppose f(x) = -x - 16. Evaluate f^-¹(-11).

Assume that f is the function with domain [-3, 3] whose graph is shown below. Estimate a number b such that f(b) + f(-b) = 2.

Choose the composite of functions that would create the graph:

Suppose . If , then find a function g such that .

Suppose . Evaluate f^-¹(4).

Choose the table that represents a function.

The Real Numbers

Linear, Quadratic, Polynomial, and Rational Functions

Exponential Functions, Logarithms, and E

Trigonometric Functions

Trigonometric Algebra and Geometry

Sequences, Series, and Limits

Polar Coordinates, Vectors, and Complex Numbers

Prelude to Calculus

Filters

Exam 2: Functions and Their Graphs

Suppose that f and g are the functions defined by the tables below. What is the range of g?

Suppose h(x) = -11 + x2, where the domain of h is the set of positive numbers. Find a formula for h-1.

Find the domain of .

Assume that for each real number x different of 0. Evaluate and simplify the expression .

Let f(x) = x2 and g(x) = x2 + 2x + 2. Which of the following alternatives best describes the relationship between the graph of f and g?

Choose the composite of functions that would create the graph:

Suppose f(x) = 5x3 + x. Which of the following alternatives equals f -1(630)?

Choose the composite of functions that would create the graph:

Suppose that f is the function defined by the table below. What is the domain of f -1?

Which of the following functions has domain ?

Suppose that g is the function defined by the table below. What is the range of g -1?

Give the coordinates of the point Using the figure below.

Assume that f is a function whose domain is the interval , whose range is the interval , and whose graph is the figure below. For g(x) = f(x + 2), A) find the domain of g. B) find the range of g. C) sketch the graph of g.

Assume that For each real number x. Evaluate and simplify the following expression.

Suppose f(x) = -x - 16. Evaluate f -1(-11).

Assume that f is the function with domain [-3, 3] whose graph is shown below. Estimate a number b such that f(b) + f(-b) = 2.

Choose the composite of functions that would create the graph:

Suppose . If , then find a function g such that .

Suppose . Evaluate f -1(4).

Choose the table that represents a function.

The Real Numbers

Linear, Quadratic, Polynomial, and Rational Functions

Exponential Functions, Logarithms, and E

Trigonometric Functions

Trigonometric Algebra and Geometry

Sequences, Series, and Limits

Polar Coordinates, Vectors, and Complex Numbers

Prelude to Calculus

Filters

Suppose h(x) = -11 + x², where the domain of h is the set of positive numbers. Find a formula for h^-¹.

Let f(x) = x² and g(x) = x² + 2x + 2. Which of the following alternatives best describes the relationship between the graph of f and g?

Suppose f(x) = 5x³ + x. Which of the following alternatives equals f^-¹(630)?

Suppose that f is the function defined by the table below. What is the domain of f ^-¹?

Suppose that g is the function defined by the table below. What is the range of g ^-¹?

Suppose f(x) = -x - 16. Evaluate f^-¹(-11).

Suppose . Evaluate f^-¹(4).