# T o explain how the graph g is obtained from the graph of f

### 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 86E
To determine

## T o explain how the graph g is obtained from the graph of f

Expert Solution

The graph g , reflect in the xaxis the part of the graph of f that is below the xaxis

### Explanation of Solution

Given information : The graph of f(x)=x24x2 and g(x)=|x24x2| are shown below

Calculation : The general rule for graphing the function g(x)=|f(x)| is to reflect all the negative values of the function f through the xaxis

That means,

f(x)=x24x2g(x)=|x24x2|g(x)=|f(x)|f(x)=x24x2g(x)=|x24x2|g(x)={x24x2;x24x20(x24x2);x24x2<0g(x)={f(x);x24x20f(x);x24x2<0g(x)={f(x);x2(x24x2)0f(x);x2(x24x2)0Y=x2(x+2)(x2)when Y is positivex2x2when Y is negative-2<x<2g(x)={f(x)    ; x2f(x) ; -2<x<2f(x)    ; x2

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