Symmetric about the y axis FUNCTIONS Symmetric about

Symmetric about the y axis FUNCTIONS Symmetric about the origin

Even functions have y-axis Symmetry 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 So for an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph.

Odd functions have origin Symmetry 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 So for an odd function, for every point (x, y) on the graph, the point (-x, -y) is also on the graph.

x-axis Symmetry We wouldn’t talk about a function with x-axis symmetry because it wouldn’t BE a function. 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7

A function is even if f( -x) = f(x) for every number x in the domain. So if you plug a –x into the function and you get the original function back again it is even. Is this function even? YES Is this function even? NO

A function is odd if f( -x) = - f(x) for every number x in the domain. So if you plug a –x into the function and you get the negative of the function back again (all terms change signs) it is odd. Is this function odd? NO Is this function odd? YES

If a function is not even or odd we just say neither (meaning neither even nor odd) Determine if the following functions are even, odd or neither. Not the original and all terms didn’t change signs, so NEITHER. Got f(x) back so EVEN.