Question 1

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

Accepted Answer

The answer of For    and  ...

Question 2

Give the coordinates of the point 
   using the figure below.

Accepted Answer

The answer of Give the coordinates of the point 
...

Question 3

Suppose    on the domain $(-\infty, \infty)$ Determine if f has an inverse.

Accepted Answer

A) True 
 B)False

Question 4

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

Accepted Answer

The answer of Suppose that f and g are the...

Question 5

Suppose    and    . Evaluate   
 .

Accepted Answer

The answer of Suppose    and  ...

Question 6

Evaluate    assuming that   and   
 .

Accepted Answer

The answer of Evaluate    assuming that ...

Question 7

Assuming that g is the function completely defined by the table below, evaluate the expression    
 .

Accepted Answer

The answer of Assuming that g is the function completely...

Question 8

Suppose 
   and $g(x) = \frac{x-3}{10}$. Determine if f and g are inverses.

Accepted Answer

A) True 
 B)False

Question 9

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 left 3 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: [-4, -1]
Par

Question 10

Assume that f is a function whose domain is the interval    , whose range is the interval   , and whose graph is the figure below. For
   
,

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 11

Suppose 
   and $g(x) = \sqrt{x-10}$. Determine if f and g are inverses.

Accepted Answer

A) True 
 B)False

Question 12

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 right 2 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, 4]
Part

Question 13

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 14

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 15

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

Accepted Answer

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

Question 16

Every odd function is one-to-one.

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

The answer of Suppose 
    . If...

Question 18

Consider the function f whose graph is shown below. Use the horizontal line test to determine if the function has an inverse.

Accepted Answer

A) True 
 B)False

Question 19

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 reflecting the graph of f in the horizontal axis.

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 20

Suppose f(x) = x7 + x5. Evaluate (f -1(13))7 + (f -1(13))5 + 13.

Accepted Answer

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

Give the coordinates of the point using the figure below.

Suppose $Suppose on the domain (-\infty, \infty) Determine if f has an inverse.$ on the domain $(-\infty, \infty)$ Determine if f has an inverse.

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

Suppose and . Evaluate .

Evaluate assuming that and .

Assuming that g is the function completely defined by the table below, evaluate the expression .

Suppose $Suppose and g(x) = \frac{x-3}{10} . Determine if f and g are inverses.$ and $g(x) = \frac{x-3}{10}$ . Determine if f and g are inverses.

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 left 3 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

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

Suppose $Suppose and g(x) = \sqrt{x-10} . Determine if f and g are inverses.$ and $g(x) = \sqrt{x-10}$ . Determine if f and g are inverses.

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 right 2 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

Choose the composite of functions that would create the graph:

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.

Every odd function is one-to-one.

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

Consider the function f whose graph is shown below. Use the horizontal line test to determine if the function has an inverse.

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 reflecting the graph of f in the horizontal axis. A) Find the domain of g B) Give a formula for g C) Find the range of g D) Sketch the graph of g

Suppose f(x) = x⁷ + x⁵. Evaluate (f^-¹(13))⁷ + (f^-¹(13))⁵ + 13.

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

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

Give the coordinates of the point using the figure below.

Suppose on the domain (−∞,∞)(-\infty, \infty)(−∞,∞) Determine if f has an inverse.

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

Suppose and . Evaluate .

Evaluate assuming that and .

Assuming that g is the function completely defined by the table below, evaluate the expression .

Suppose and g(x)=x−310g(x) = \frac{x-3}{10}g(x)=10x−3​ . Determine if f and g are inverses.

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 left 3 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

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

Suppose and g(x)=x−10g(x) = \sqrt{x-10}g(x)=x−10​ . Determine if f and g are inverses.

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 right 2 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

Choose the composite of functions that would create the graph:

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.

Every odd function is one-to-one.

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

Consider the function f whose graph is shown below. Use the horizontal line test to determine if the function has an inverse.

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 reflecting the graph of f in the horizontal axis. A) Find the domain of g B) Give a formula for g C) Find the range of g D) Sketch the graph of g

Suppose f(x) = x7 + x5. Evaluate (f -1(13))7 + (f -1(13))5 + 13.

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 $Suppose on the domain (-\infty, \infty) Determine if f has an inverse.$ on the domain $(-\infty, \infty)$ Determine if f has an inverse.

Suppose $Suppose and g(x) = \frac{x-3}{10} . Determine if f and g are inverses.$ and $g(x) = \frac{x-3}{10}$ . Determine if f and g are inverses.

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 left 3 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

Suppose $Suppose and g(x) = \sqrt{x-10} . Determine if f and g are inverses.$ and $g(x) = \sqrt{x-10}$ . Determine if f and g are inverses.

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 right 2 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 reflecting the graph of f in the horizontal axis. A) Find the domain of g B) Give a formula for g C) Find the range of g D) Sketch the graph of g

Suppose f(x) = x⁷ + x⁵. Evaluate (f^-¹(13))⁷ + (f^-¹(13))⁵ + 13.