# The x- and y- intercepts for the equation x = | y | and test the symmetry of the equation. Also construct the table to sketch the graph of the equation.

BuyFind

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.8, Problem 74E
To determine

Expert Solution

## Answer to Problem 74E

The x-intercept is 0 and y-intercept is 0 . The equation is symmetric about x-axis.Graph of the equation x=|y| is provided below,

### Explanation of Solution

Given information:

The equation x=|y| .

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.

The x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

The y-intercepts are the points on y-axis where the graph of the equation intersects the y-axis.

Calculation:

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

Substitute the point x=0 in the equation x=|y| ,

0=|y|y=0

Substitute the point x=1 in the equation x=|y| ,

1=|y|y=±1

Substitute the point x=2 in the equation x=|y| ,

2=|y|y=±2

Construct a table with the values obtained above,

xy(x,y)00(0,0)11(1,1)11(1,1)22(2,2)

In the coordinate plane plot the points obtained above and connect them through a line.

The graph of the equation is provided below x=|y| .

Recall that the x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

Substitute y=0 in the equation x=|y| ,

0=|y|y=0

Therefore, x-intercept is 0.

Recall that the y-intercepts are the points on x-axis where the graph of the equation intersects the y-axis.

Substitute x=0 in the equation x=|y| ,

0=|y|y=0

Therefore, y-intercept is 0 .

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=|y| ,

x=|y|x=|y|

The equation is unchanged. Therefore, the equation y=4|x| 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=|y| ,

x=|y|

The equation is changed. Therefore, the equation x=|y| 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=|y| ,

x=|y|x=|y|

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

Thus, the x-intercept is 0 and y-intercept is 0 . The equation is symmetric about x-axis.Graph of the equation x=|y| is provided below,

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