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 111RE
To determine

To graph: The equation y=23x and check the equation for symmetry.

Expert Solution

Answer to Problem 111RE

The equation y=23x is not symmetric and the graph is as follows:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 111RE , additional homework tip  1

Explanation of Solution

Given information:

The equation of line y=23x

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 y=23x (1)

Firstly replace y by y in (1)

  y=23xy=2+3x

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

Hence, y=23x is not symmetric about x -axis

Next, replace x by x in (1)

  y=23(x)y=2+3x

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

Hence, y=23x is not symmetric about y -axis.

Thus, y=23x is not symmetric about origin.

For plotting:

    xy=23x(x.y)
    012214(0,2)(1,1)(2,4)

We plot these points to get the graph as follows:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 111RE , additional homework tip  2

Thus, y=23x is neither symmetric about x -axis nor about y -axis.

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