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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.8, Problem 67E

To determine

**To calculate: **The x- and y- intercepts for the equation

Expert Solution

There are __nox__-intercepts and y-intercepts. The equation is __symmetric about origin__. Graph of the equation is provided below,

**Given information:**

The equation

**Formula used:**

The function is symmetric about the x-axis, when y is replaced by

The function is symmetric about the y-axis, when x is replaced by

The function is symmetric with respect to origin, when y is replaced by

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

Substitute the point

Substitute the point

Substitute the point

Substitute the point

Construct a table with the values obtained above,

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

The graph of the equation is provided below

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

Substitute

Therefore, there are no x-intercepts.

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

Substitute

Therefore, there are noy-intercepts.

Recall that the function is symmetric about the x-axis, when y is replaced by

Replace y by

The equation is changed. Therefore, the equation

Recall that the function is symmetric about the y-axis, when x is replaced by

Replace x by

The equation is changed. Therefore, the equation

Recall that the function is symmetric with respect to origin, when y is replaced by

Replace x by

The equation is unchanged. Therefore, the equation

Thus, there are nox-intercepts and y-intercepts. The equation is symmetric about origin.Graph of the equation