FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin

So for an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph. f(-x) = f(x) Even functions have y-axis Symmetry

So for an odd function, for every point (x, y) on the graph, the point (-x, -y) is also on the graph. f(-x) = - f(x) Odd functions have origin Symmetry

We wouldn’t talk about a function with x-axis symmetry because it wouldn’t BE a function. x-axis Symmetry

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.

8 Increasing and Decreasing Functions

A function f is increasing on an interval if as x increases, then f ( x ) increases. A function f is decreasing on an interval if as x increases, then f ( x ) decreases. f ( x ) is increasing in the interval. vertex (1.5,-2) f ( x ) is decreasing in the interval. Increasing/Decreasing Functions

Increasing, Decreasing, Constant Intervals Find the interval(s) over which the interval is increasing, decreasing and constant? Answer Now A function f is constant on an interval if as x increases, then f ( x ) remains the same.

Find the interval(s) over which the interval is increasing, decreasing and constant? Increasing, Decreasing, Constant Intervals Answer Now