Symmetry

This section is on symmetry. There are four places you can check for symmetry: the x-axis, the y-axis, the origin, and the line y=x.

Things you need to know are as follows:

I. X-axis

• Put a negative in front of the y's and simplify.
  
• It is symmetric about the x-axis if it matches the original problem.

II. Y-axis:

• Put a (-) in front of the x's.
  
• It is symmetric about the y-axis if it matches the original problem.

III. Origin:

• Put a (-) in front of the x's and a negative in front of the y's.
• It is symmetric about the origin if it matches the original problem.

IV. Y=x

• Switch the x and y.
• Solve for y.
• It is symmetric about the line y=x if it matches the original problem.

Example 1: y=x^2 - 8

I. -y=x^2 - 8. y=-x^2 + 8. Since the new equation is not the same as the original: not symmetric about the x-axis.

II. y=(-x^2) - 8. y=x^2 - 8. Since the new equation is the same as the original: symmetric about the y-axis.

III. -y=(-x^2) - 8. -y=x^2 - 8. y=-x^2 + 8. Since the new equation is not the same as the original: not symmetric about the origin.

IV. x=y^2 -8. y= square root of x + 8. Since the new equation is not the same as the original: not symmetric about the line y=x.

Amber :)