# 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 51E
To determine

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

Expert Solution

The equation of the final transformed graph is g(x)=x4+1 .

### Explanation of Solution

Given information :

The function is f(x)=x4 .

Concept used:

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 reflected in the y- axis , then the equation of the transformed graph will be g(x)=f(x) .

The function is given as: f(x)=x4

The graph of g(x) is obtained by reflecting the graph of f(x)=x4 in they- axis then shift 1 unitsupward.

Use definition of reflectingand vertically shifting of the graph,

Therefore,

The equation of the final transformed graph is obtained as:

g(x)=f(x)+c

Substitute, f(x)=x4 and c=1 ,

g(x)=x4+1

Hence,

The equation of the final transformed graph is g(x)=x4+1 .

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