# Whether the equation x = y 4 − y 2 is symmetric about x-axis or y-axis or origin.

### 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 1.8, Problem 78E
To determine

## To calculate:Whether the equation x=y4−y2 is symmetric about x-axis or y-axis or origin.

Expert Solution

The equation x=y4y2 is symmetric only with respect to x-axis.

### Explanation of Solution

Given information:

The equation x=y4y2 .

Formula used:

The function is symmetric about the x-axis, when y is replaced by y , the equation remains unchanged.

The function is symmetric about the y-axis, when x is replaced by x , the equation remains unchanged.

The function is symmetric with respect to origin, when y is replaced by y and x is replaced by x , the equation remains unchanged.

Calculation:

It is provided that the equation is x=y4y2 . Construct a table to evaluate the value of y for different values of x.

Recall that the function is symmetric about the x-axis, when y is replaced by y , the equation remains unchanged.

Replace y by y in the equation x=y4y2 ,

x=(y)4(y)2x=y4y2

The equation is unchanged. Therefore, the equation x=y4y2 is symmetricabout the x-axis.

Recall that the function is symmetric about the y-axis, when x is replaced by x , the equation remains unchanged.

Replace x by x in the equation x=y4y2 ,

x=y4y2

The equation is changed. Therefore, the equation x=y4y2 is not symmetricabout the y-axis.

Recall that the function is symmetric with respect to origin, when y is replaced by y and x is replaced by x , the equation remains unchanged.

Replace x by x and y by y in the equation x=y4y2 ,

x=(y)4(y)2x=y4y2

The equation is changed. Therefore, the equation x=y4y2 is not symmetricabout the origin.

Thus, the equation is symmetric only about x-axis.

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