# The x- and y- intercepts for the equation y = | 4 − x | and test the symmetry of the equation. Also construct the table to sketch the graph of the equation.

### 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 76E
To determine

## To calculate: The x- and y- intercepts for the equation y=|4−x| and test the symmetry of the equation. Also construct the table to sketch the graph of the equation.

Expert Solution

The x-intercept is 4 and y-intercept is 4 . No axis of symmetry.Graph of the equation y=|4x| is provided below,

### Explanation of Solution

Given information:

The equation y=|4x| .

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 y=|4x| . Construct a table to evaluate the value of y for different values of x.

Substitute the point x=0 in the equation y=|4x| ,

y=|40|y=4

Substitute the point x=1 in the equation y=|4x| ,

y=|41|y=3

Substitute the point x=2 in the equation y=|4x| ,

y=|42|y=2

Substitute the point x=4 in the equation y=|4x| ,

y=|44|y=0

Construct a table with the values obtained above,

xy(x,y)04(0,4)13(1,3)22(2,2)40(4,0)

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

The graph of the equation is provided below y=|4x| .

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 y=|4x| ,

0=|4x|4x=0x=4

Therefore, x-intercepts is 4 .

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 y=|4x| ,

y=|40|y=4

Therefore, y-intercept is 4 .

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 y=|4x| ,

y=|4x|

The equation is changed. Therefore, the equation y=|4x| is not 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 y=|4x| ,

y=|4(x)|y=|4+x|

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

y=|4(x)|y=|4+x|

The equation is changed. Therefore, the equation y=|4x| is not symmetricabout the origin.

Thus, the x-intercept is 4 and y-intercept is 4 . No axis of symmetry.Graph of the equation y=|4x| is provided below,

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