Math Symmetry Question!!

Question

Use the algebraic tests to check for symmetry with respect to both axes and the origin.

1. y = -4x + 2
2. y = x² + 2
3. y = - IxI - 2

Answer 1

The way to check for symmetry is to substitute into the original equation

and see if after you simplify the equation is equivalent to the original.

1) To check for symmetry about the X axis

replace the Y in the equation with a -Y.

Then simplify and see if it is equivalent to the original.

ex:

y = -5x - 4

-y = -5x - 4

y = 5x + 4

This is NOT equivalent so it Is NOT symmetric about the X axis.

2) To check for symmetry about the Y axis

replace the X in the equation with a -X.

ex:

y = x⁴ + 7

y = (-x)⁴ + 7

y = x⁴ + 7

This IS equivalent so it IS symmetric about the Y axis

3) To check for symmetry about the origin

replace both the X and Y in the equation with a -X and -Y

Then simplify and see if it is an equivalent equation.

Note: To check for symmetry about X replace the Y

and to check for symmetry about Y replace the X.

Opposites. You can use that as hint to remember.