Even functions satisfy f(-x) = f(x); their graphs are symmetric about the y-axis. Examples: $x^2$, |x|, cos(x). Odd functions satisfy f(-x) = -f(x); their graphs are symmetric about the origin. Examples: $x^3$, sin(x), tan(x). The domain must be symmetric about 0 for either property. f(x) = 0 is the only function that is both even and odd. Any function can be decomposed: f(x) = g(x) + h(x) where g(x) = (f(x)+f(-x))/2 is even and h(x) = (f(x)-f(-x))/2 is odd. Periodic functions satisfy f(x+T) = f(x) for some smallest positive T (fundamental period). Common periods: sin/cos have 2*pi, tan/cot have pi.