# To graph the functionson the same screen and how they related to the graph in part (a). The functions are given below: f ( x ) = 2 x − x 2 ( a ) y 1 = f ( x ) ( b ) y 2 = f ( − x ) ( c ) y 3 = − f ( − x ) ( d ) y 4 = f ( − 2 x ) ( e ) y 5 = f ( − 1 2 x )

### 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 74E
To determine

## To graph the functionson the same screen and how they related to the graph in part (a).The functions are given below:  f(x)=2x−x2(a) y1=f(x)(b)y2=f(−x)(c)y3=−f(−x)(d)y4=f(−2x)(e)y5=f(−12x)

Expert Solution

### Explanation of Solution

Given information:

The function are:

f(x)=2xx2(a) y1=f(x)(b)y2=f(x)(c)y3=f(x)(d)y4=f(2x)(e)y5=f(12x)

Graph :

the graph obtained as:

Interpretation: from the above graph it is observed that for part(b) symmetric graph of part (a) about y -axis.

For part (c) symmetric graph of part (a) about y -axis and reflect about x -axis.

For part (d) symmetric graph of part (a) about y -axis and shrink horizontally by the factor of 12 .

For the part (e) symmetric graph of part (a) about y -axis and stretch horizontally by the factor of 2.

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