1. Equal distance from origin.
EVEN FUNCTION: when the “directed distance” from the x-axis to the graph of the function is equal to the right and left of the origin f(-x) = f(x). They are symmetric about the y-axis. x y -5 5
f(5)
f(-5)
Equal distance above the x-axis.
Equal distance from origin.

2. Equal distance from origin.
ODD FUNCTION: when the “directed distance” from the x-axis to the graph of the function is equal but in opposite directions to the right and left of the origin f(-x) = -f(x). They are symmetric about the origin. y
Equal distance but opposite directions.
f(-5)
f(5) -5 x 5
Equal distance from origin.

3. If all the terms of a function are even, then the function is even
If all the terms of a function are even, then the function is even. f(-x) = f(x)
f(x) = x4 + x2
f(-x) = (-x)4 + (-x)2 = x4 + x2 = f(x)
If all the terms of a function are odd, then the function is odd. f(-x) = -f(x)
f(x) = x3 + 2x
f(-x) = (-x)3 + 2(-x) = -(x3 + 2x) = -f(x)

4. NEITHER: graphs that are not symmetric about the y-axis or the origin are neither even nor odd.