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 59E
To determine

To calculate: The x- and y- intercepts for the equation 2xy=6 and test the symmetry of the equation. Also construct the table to sketch the graph of the equation.

Expert Solution

Answer to Problem 59E

The x-intercept is 3 and y-intercept is 6 . The equation is neither symmetric about x-axis, nor y-axis nor origin. Graph of the equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 59E , additional homework tip  1

Explanation of Solution

Given information:

The equation 2xy=6 .

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 2xy=6 . Construct a table to evaluate the value of y for different values of x.

Substitute the point x=0 in the equation 2xy=6 ,

  2(0)y=6y=6

Substitute the point x=1 in the equation y=3x+3 ,

  2(1)y=6y=26y=4

Substitute the point x=2 in the equation y=3x+3 ,

  2(2)y=6y=46y=2

Substitute the point x=3 in the equation y=3x+3 ,

  2(3)y=6y=66y=0

Construct a table with the values obtained above,

  xy(x,y)06(0,6)14(1,4)22(2,2)30(3,0)

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

The graph of the equation is provided below 2xy=6 .

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 59E , additional homework tip  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 2xy=6 ,

  2x(0)=62x=6x=3

Therefore, x-intercept is 3.

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 2xy=6 ,

  2(0)(y)=6y=6

Therefore, y-intercept is 6 .

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 2xy=6 ,

  2x(y)=62x+y=6

The equation is changed. Therefore, the equation 2xy=6 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 2xy=6 ,

  2(x)y=62xy=6

The equation is changed. Therefore, the equation 2xy=6 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 2xy=6 ,

  2(x)(y)=62x+y=6

The equation is changed. Therefore, the equation 2xy=6 is not symmetricabout the origin.

Thus, the x-intercept is 3 and y-intercept is 6 . The equation is neither symmetric about x-axis, nor y-axis nor origin. Graph of the equation 2xy=6 is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 59E , additional homework tip  3

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