Calculus

A function is a rule that assigns each element in a set D to exactly one element in a set R.

If f is an even function, then f(-x) = f(x) for all x. If f is an odd function, then f(-x) = -f(x) for all x. f(x) = x^2 is an even function because f(-x) = (-x)^2 = (-x)(-x) = x^2 = f(x). f(x) = x^3 is an odd function because f(-x) = (-x)^3 = (-x)(-x)(-x) = (-x)x^2 = -(x^3) = -f(x). Odd functions are symmetric with respect to the origin. Even functions are symmetric with respect to the y-axis.

A function is called increasing on an interval I if for all x1 < x2 in I, f(x1) < f(x2). And a function is called decreasing on an interval I if for all x1 < x2 in I, f(x1) > f(x2).