To graph: the function f ( x ) = 3 | x | using the graph of a standard function and then applying transformations.

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 2.5, Problem 35E
To determine

To graph: the function f(x)=3|x| using the graph of a standard function and then applying transformations.

Expert Solution

Explanation of Solution

Given information:

the function is f(x)=3|x|

Graph:

To plot the graph of f(x)=|x| ,use the plotting points method, substitute different value of x on f(x)=|x| to determine corresponding value of f(x) .

The table is thus obtained as:

 x -2 -1 1 2 y 2 1 1 2

now plot each point of x along the horizontal axis and the corresponding value of f(x)=y along vertical axis and connect each point to form a smooth curve.

The graph of f(x)=|x| is obtained as:

Now, the graph of f(x)=3|x| is the graph of f(x)=|x| stretchedvertically by a factor of 3 .

The graphof f(x)=3|x| is obtained as:

Interpretation:

From the above graph it can be obtained that the graph of f(x)=3|x| is obtained by stretching the graph of f(x)=|x| vertically by a factor of 3 .

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