odd functions what is their common characteristic? they have point symmetry about the origin

ODD FUNCTIONS What is their common characteristic? They have point symmetry about the origin.

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y = x 3 ODD y = (x- 3) 3 NEITHER ODDNEITHER Stretches & reflections do not change odd symmetry, but all other transformations do.

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ODD FUNCTIONS

What is their common characteristic?They have point symmetry about the origin.

EVEN FUNCTIONS

What is their common characteristic?

They have line symmetry over the y-axis.

y = x3

ODDy = (x- 3)3

NEITHER

5 XyODD

3Xy 5 NEITHER

Stretches & reflections do not change odd symmetry, but all other transformations do.

Page 4: ODD FUNCTIONS What is their common characteristic? They have point symmetry about the origin

y = x4

EVEN y = x4 - 3 EVEN

Vertical shifts do NOT change even symmetry.

y = (x – 3)4 NEITHER

Horizontal shifts change even symmetry to neither.

Stretches and reflections do not change even symmetry.

Page 5: ODD FUNCTIONS What is their common characteristic? They have point symmetry about the origin

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