Equal distance from origin.

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Presentation transcript:

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.

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.

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)

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