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, Problem 117RE
To determine

To graph: The equation x=y and check the equation for symmetry.

Expert Solution

Answer to Problem 117RE

The equation x=y is not symmetric and the graph is as follows:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 117RE , additional homework tip  1

Explanation of Solution

Given information:

The equation of line x=y

Formula used:

The equation is said to have symmetry about the x -axis when the equation remains unchanged on replacing y by y

Graphically it can be said that the graph remains unchanged when reflected in the x -axis.

The equation is said to have symmetry about the y -axis when the equation remains unchanged on replacing x by x

Graphically it can be said that the graph remains unchanged when reflected in the y -axis.

The equation is said to have symmetry about the origin if it is symmetric about x -axis and y -axis that is the equation remains unchanged on replacing x by x or y by y

Graphically it can be said that the graph remains unchanged when rotated with an angle of 180 about the origin.

Calculation:

It is provided that the equation of line is x=y (1)

Firstly replace y by y in (1)

  x=y

The equation obtained is not the same as the original one.

Hence, x=y is not symmetric about x -axis

Next, replace x by x in (1)

  x=yx=y

The equation obtained is not the same as the original one.

Hence, x=y is not symmetric about y -axis.

Thus, x=y is not symmetric about origin.

For plotting:

    xx=y(x.y)
    022044(0,0)(2,4)(2,4)

We plot these points to get the graph as follows:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 117RE , additional homework tip  2

Thus, x=y is neither symmetric about x -axis nor about y -axis.

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