# The x- and y- intercepts for the equation x y = 2 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 67E
To determine

## To calculate: The x- and y- intercepts for the equation xy=2 and test the symmetry of the equation. Also construct the table to sketch the graph of the equation.

Expert Solution

There are nox-intercepts and y-intercepts. The equation is symmetric about origin. Graph of the equation is provided below,

### Explanation of Solution

Given information:

The equation xy=2 .

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 xy=2 . Construct a table to evaluate the value of y for different values of x.

Substitute the point x=1 in the equation xy=2 ,

(1)y=2y=2

Substitute the point x=2 in the equation xy=2 ,

(2)y=2y=1

Substitute the point x=3 in the equation xy=2 ,

(3)y=2y=23

Substitute the point x=4 in the equation xy=2 ,

(4)y=2y=12

Construct a table with the values obtained above,

xy(x,y)12(1,2)21(2,1)323(3,23)412(4,12)

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

The graph of the equation is provided below xy=2 .

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 xy=2 ,

(0)x=2x=20

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 x=0 in the equation xy=2 ,

(0)y=2y=20

Therefore, there are noy-intercepts.

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 xy=2 ,

x(y)=2xy=2

The equation is changed. Therefore, the equation y=9x2 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 xy=2 ,

(x)y=2xy=2

The equation is changed. Therefore, the equation xy=2 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 xy=2 ,

(x)(y)=2xy=2

The equation is unchanged. Therefore, the equation xy=2 is symmetricabout the origin.

Thus, there are nox-intercepts and y-intercepts. The equation is symmetric about origin.Graph of the equation xy=2 is provided below,

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