# 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 52E
To determine

Expert Solution

## Answer to Problem 52E

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

### Explanation of Solution

Given information :

The function is f(x)=x2 .

Concept used:

If the graph of y=f(x) is shifted horizontallyleft 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 x- axis , then the equation of the transformed graph will be g(x)=f(x) .

The function is given as: f(x)=x2

The graph of g(x) is obtained by reflecting the graph of f(x)=x2 in thex- axis then shift 2 unitsleft.

Use definition of reflectingand horizontallyshifting of the graph,

Therefore,

The equation of the final transformed graph is obtained as:

g(x)=f(x+c)

Substitute, f(x)=x2 and c=2 ,

g(x)=(x+2)2

Hence,

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

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