Question 1

If f is the function with domain [-2, 2] whose graph is shown below, then $f\left(\frac{1}{2}\right) \geq f\left(-\frac{1}{2}\right)$.

Accepted Answer

A) True 
 B)False

Question 2

Let f(x) = x2 - x3 with domain [-1, 2] and range [-4, 2], whose graph is shown below. The graph of g is obtained by stretching the graph of f by a factor of
  in the horizontal direction.

A) Find the domain of g
B) Give a formula for g
C) Find the range of g
D) Sketch the graph of g

Accepted Answer

Part A: [-1/4, 1/2]
...

Question 3

The graph of f(x)  is shown below, its domain is [-2, 3]. Find the domain of g(x)  = f(2x + 1) ?

Accepted Answer

A)   [-1, 4]
B)   [1, 7]
C)   
D)   [-3, 2]

Question 4

Suppose h(x) = -6 - 2x2, where the domain of h is the set of positive numbers. Find a formula for h-1.

Accepted Answer

Question 5

Consider the function f with domain [0, 12] whose graph is shown below.
  
A) What is the largest interval contained in the domain of f on which f is increasing?
B) Let g denote the function obtained from f by restricting the domain to the interval in part (a). What is the domain of g -1 ?

Accepted Answer

Part A: [3...

Question 6

Evaluate   assuming that  and  
 .

Accepted Answer

The answer of Evaluate   assuming that  and...

Question 7

Suppose 
   . If f(x) = (x + 9)2, then find a function g such that  
 .

Accepted Answer

Question 8

Given   . Find the value(s)  of x such that f(x)  = 1.
I
 
II
 
III

Accepted Answer

A)   I
B)   II
C)   III
D)   I and III

Question 9

If f is defined by the first table of values, then  is defined for the last table of values, regardless the value of k.

Accepted Answer

A) True 
 B)False

Question 10

For   and  , find a formula for   . Simplify your results as much as possible.

Accepted Answer

The answer of For   and  , find...

Question 11

For   and  , find a formula for   . Simplify your results as much as possible.

Accepted Answer

The answer of For   and  , find...

Question 12

For   and  , find a formula for   . Simplify your results as much as possible.

Accepted Answer

The answer of For   and  , find...

Question 13

Assume that 
   . Find a number b such that
  
 .

Accepted Answer

The answer of Assume that 
   . Find...

Question 14

If f(x) = 6x + b and g(x) = 6x + c, then f  g = g f if and only if b = c.

Accepted Answer

A) True 
 B)False

Question 15

If the function f is given by the following table, then $f^{ -1}$ can be represented by the adjacent graph.

Accepted Answer

A) True 
 B)False

Question 16

Let f(x) = x2 - x3 with domain [-1, 2] and range [-4, 2], whose graph is shown below. The graph of g is obtained by shifting the graph of f up 4 units.

A) Find the domain of g
B) Give a formula for g
C) Find the range of g
D) Sketch the graph of g

Accepted Answer

Part A: [-1, 2]
Part...

Question 17

Evaluate Assuming that And  
 .

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Suppose 
   . Find the domain of f -1.

Accepted Answer

Question 19

Assume that 
  for all real numbers x not equal to -7. Evaluate and simplify the expression.

Accepted Answer

The answer of Assume that 
  for all real...

Question 20

Find a number c such that , where 
And   .

Accepted Answer

A)   241
B)   -239
C)   -209
D)   -210

Exam 2: Functions and Their Graphs

Consider the function f with domain [0, 12] whose graph is shown below. A) What is the largest interval contained in the domain of f on which f is increasing? B) Let g denote the function obtained from f by restricting the domain to the interval in part (a). What is the domain of g -1 ?

Correct AnswerverifiedPart A: [3...View AnswerShow Answer

If f(x) = 6x + b and g(x) = 6x + c, then f g = g 11eecfcf_3157_7930_ac77_83cb757619bc_TB10659_11f if and only if b = c.

Correct AnswerverifiedShow Answer

If f is defined by the first table of values, then is defined for the last table of values, regardless the value of k.

Correct AnswerverifiedShow Answer

Assume that . Find a number b such that .

Correct AnswerverifiedShow Answer

Suppose . If f(x) = (x + 9)2, then find a function g such that .

Correct AnswerverifiedShow Answer

Let f(x) = x2 - x3 with domain [-1, 2] and range [-4, 2], whose graph is shown below. The graph of g is obtained by stretching the graph of f by a factor of in the horizontal direction. A) Find the domain of g B) Give a formula for g C) Find the range of g D) Sketch the graph of g

Correct AnswerverifiedPart A: [-1/4, 1/2]...View AnswerShow Answer

If f is the function with domain [-2, 2] whose graph is shown below, then f(12)≥f(−12)f\left(\frac{1}{2}\right) \geq f\left(-\frac{1}{2}\right)f(21​)≥f(−21​) .

Correct AnswerverifiedShow Answer

For and , find a formula for . Simplify your results as much as possible.

Correct AnswerverifiedShow Answer

Let f(x) = x2 - x3 with domain [-1, 2] and range [-4, 2], whose graph is shown below. The graph of g is obtained by shifting the graph of f up 4 units. A) Find the domain of g B) Give a formula for g C) Find the range of g D) Sketch the graph of g

Correct AnswerverifiedPart A: [-1, 2]Part...View AnswerShow Answer

Find a number c such that , where And .

Correct AnswerverifiedShow Answer

For and , find a formula for . Simplify your results as much as possible.

Correct AnswerverifiedShow Answer

Evaluate assuming that and .

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If the function f is given by the following table, then f−1f^{ -1}f−1 can be represented by the adjacent graph.

Correct AnswerverifiedShow Answer

The graph of f(x) is shown below, its domain is [-2, 3]. Find the domain of g(x) = f(2x + 1) ?

Correct AnswerverifiedShow Answer

Suppose . Find the domain of f -1.

Correct AnswerverifiedShow Answer

Evaluate Assuming that And .

Correct AnswerverifiedShow Answer

For and , find a formula for . Simplify your results as much as possible.

Correct AnswerverifiedShow Answer

Given . Find the value(s) of x such that f(x) = 1. I II III

Correct AnswerverifiedShow Answer

Assume that for all real numbers x not equal to -7. Evaluate and simplify the expression.

Correct AnswerverifiedShow Answer

Suppose h(x) = -6 - 2x2, where the domain of h is the set of positive numbers. Find a formula for h-1.

Correct AnswerverifiedShow Answer

Consider the function f with domain [0, 12] whose graph is shown below. A) What is the largest interval contained in the domain of f on which f is increasing? B) Let g denote the function obtained from f by restricting the domain to the interval in part (a). What is the domain of g ^-¹ ?

Correct Answer
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Part A: [3...
View Answer

Correct Answer
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Correct Answer
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Suppose . If f(x) = (x + 9)², then find a function g such that .

Correct Answer
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Let f(x) = x² - x³ with domain [-1, 2] and range [-4, 2], whose graph is shown below. The graph of g is obtained by stretching the graph of f by a factor of in the horizontal direction. A) Find the domain of g B) Give a formula for g C) Find the range of g D) Sketch the graph of g

Correct Answer
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Part A: [-1/4, 1/2]
...
View Answer

If f is the function with domain [-2, 2] whose graph is shown below, then $f\left(\frac{1}{2}\right) \geq f\left(-\frac{1}{2}\right)$ . $If f is the function with domain [-2, 2] whose graph is shown below, then f\left(\frac{1}{2}\right) \geq f\left(-\frac{1}{2}\right) .$

Correct Answer
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Correct Answer
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Let f(x) = x² - x³ with domain [-1, 2] and range [-4, 2], whose graph is shown below. The graph of g is obtained by shifting the graph of f up 4 units. A) Find the domain of g B) Give a formula for g C) Find the range of g D) Sketch the graph of g

Correct Answer
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Part A: [-1, 2]
Part...
View Answer

Correct Answer
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Correct Answer
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Correct Answer
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If the function f is given by the following table, then $f^{ -1}$ can be represented by the adjacent graph. $If the function f is given by the following table, then f^{ -1} can be represented by the adjacent graph.$

Correct Answer
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Correct Answer
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Suppose . Find the domain of f^-¹.

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Suppose h(x) = -6 - 2x², where the domain of h is the set of positive numbers. Find a formula for h^-¹.

Correct Answer
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