BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.3, Problem 6E

a.

To determine

To calculate: the values of g(2),g(0) and g(7)

Expert Solution

Answer to Problem 6E

  g(2)=4g(0)=7g(7)=4

Explanation of Solution

Given information: the graph of function g is provided,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  1

Graph:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  2

Interpretation:

In the graph, the value of g(2) is the corresponding y- value at x = 2 , that is,

  g(2)=4

Similarly, the corresponding y -values for,

  g(0) at x = 0 is 7

  g(7) at x = 7 is 4

Hence,

  g(2)=4g(0)=7g(7)=4

b.

To determine

the domain and the range of the provided graph

Expert Solution

Answer to Problem 6E

The domain and range of g is [-2,8] and [2,7], respectively.

Explanation of Solution

Given information: the graph of function g is provided,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  3

Graph:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  4

Interpretaion:

The domain of the function g is all the x -values of the points on the graph, and the range is all the corresponding y -values.

From the graph of g , we see that the domain of g is the interval [-2, 8] and the range of g is the interval [2, 7].

Hence, the domain and range of g is [-2,8] and [2,7], respectively.

c.

To determine

To calculate: the value of x for which g ( x ) = 4

Expert Solution

Answer to Problem 6E

the value of x for which g ( x ) = 3 is 2,2,7 .

Explanation of Solution

Given information: the graph of function g is provided,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  5

Graph:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  6

The function value of g ( a ) from the graph of g , is the height of the graph above the x -axis at x = a ,

Therefore, g ( x ) = 4 is the x -value on the x -axis where the height above it is 4, that are,

  g(2)=4g(2)=4g(7)=4

hence, the value of x for which g ( x ) = 3 is 2,2,7 .

d.

To determine

To calculate: the values for g(x)>4

Expert Solution

Answer to Problem 6E

the values of x for g(x)>4 are 1x1 and x = 8

Explanation of Solution

Given information: the graph of function h is provided,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  7

Graph:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 6E , additional homework tip  8

Interpretation:

When g(x)>4 is expressed in words it means, g ( x ) is more than to 4. From the graph, write all the x -values whose corresponding y -values are more than 4.

Therefore, the x-values from the graph for g(x)>4 ,

  g(1),g(0),g(1),g(8)

Hence, the values of x for g(x)>4 are 1x1 and x = 8

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