# 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 50E
To determine

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

Expert Solution

The equation of the final transformed graph is g(x)=|x+4|2 .

### Explanation of Solution

Given information :

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

Concept used:

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

If the graph of y=f(x) is shifted vertically downward 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 left the graph of f(x)=|x| by 4 units and then shift 2 unit downward.

Use definition of horizontallyand vertically shifting of the graph,

Therefore,

The equation of the final transformed graph is obtained as:

g(x)=f(x+c)d

Substitute, f(x)=|x| and c=4 , d=2

g(x)=|x+4|2

Hence,

The equation of the final transformed graph is g(x)=|x+4|2 .

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