# To write the equation of the final transformed graph.

### 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 49E
To determine

## To write the equation of the final transformed graph.

Expert Solution

The equation of the final transformed graph is g(x)=|x3|+1 .

### Explanation of Solution

Given information :

The function is f(x)=|x| .

Concept used:

If the graph of y=f(x) is shifted horizontalright by c unit, then the equation of the transformed graph will be g(x)=f(xc)

If the graph of y=f(x) is shifted vertically upward by c unit, then the equation of the transformed graph will be g(x)=f(x)+c

The function is given as: f(x)=|x|

The graph of g(x) is obtained by shifting right the graph of f(x)=|x| by 3 units and then shift 1 unit upward.

Use definition of horizontallyand vertically shifting of the graph,

Therefore,

The equation of the final transformed graph is obtained as:

g(x)=f(xc)+d

Substitute, f(x)=|x| and c=3 , d=1

g(x)=|x3|+1

Hence,

The equation of the final transformed graph is g(x)=|x3|+1 .

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