# 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 54E
To determine

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

Expert Solution

The equation of the final transformed graph is g(x)=12|x1|+3 .

### Explanation of Solution

Given information :

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

Concept used:

If the graph of y=f(x) is shifted horizontallyright 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 .

If the graph of y=f(x) is shrink vertically by a factor of c unit, then the equation of the transformed graph will be g(x)=cf(x) .

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

The graph of g(x) is obtained by shrink the graph of f(x)=|x| vertically by a factor of 12 unit then shift 1 unitsright and then shift 3 unit upwards.

Use definition of horizontally, vertically shifting and shrinking vertically of the graph,

Therefore,

The equation of the final transformed graph is obtained as:

g(x)=d·f(xc)+e

Substitute, f(x)=|x| and c=1,d=12 and e=3 ,

g(x)=12|x1|+3

Hence,

The equation of the final transformed graph is g(x)=12|x1|+3 .

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