Question 1

Suppose 
    . Find the domain of f -1.

Accepted Answer

Question 2

Find a number c such that  , where  
And    .

Accepted Answer

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

Question 3

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

Accepted Answer

The answer of For    and  ...

Question 4

Evaluate    assuming that   and   
 .

Accepted Answer

The answer of Evaluate    assuming that ...

Question 5

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

Accepted Answer

The answer of For    and  ...

Question 6

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 7

Evaluate  Assuming that  And   
 .

Accepted Answer

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

Question 8

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

Accepted Answer

The answer of For    and  ...

Question 9

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...

Question 10

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 11

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

Accepted Answer

Question 12

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 13

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

Question 14

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 15

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 16

Assume that 
    . Find a number b such that
   
 .

Accepted Answer

The answer of Assume that 
    ....

Question 17

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 18

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 19

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

Question 20

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

Suppose . Find the domain of f^-¹.

Find a number c such that , where And .

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

Evaluate assuming that and .

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

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

Evaluate Assuming that And .

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

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

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

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

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 ?

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

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

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

Assume that . Find a number b such that .

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

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

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

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.

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 . Find the domain of f -1.

Find a number c such that , where And .

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

Evaluate assuming that and .

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

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

Evaluate Assuming that And .

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

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

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​) .

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

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 ?

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

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

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

Assume that . Find a number b such that .

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

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

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

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.

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 . Find the domain of f^-¹.

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

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

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

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 ?

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

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

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