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

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Presentation transcript:

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

y = x 4 EVEN y = x 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.

Inverse Equations To graph –Make a table for the equation –Invert the x and y values to graph the inverse To write an equation –Switch the x & y variables –Solve –Look for restrictions