 Even and odd functions: A function f(x) is said to be an even function if f(x) = f(x), f(x) = x^{2} and g(x) = cos x are examples of even functions. If (x,f(x)) is a point on the graph then (x,f(x)) is also on the graph.
A function f(x) is said to be an odd function if f(x) = f(x), f = x^{3} and g(x) = sin x are examples of odd functions. Odd functions are symmetric with respect to origin. If (x,f(x)) is a point on the graph then (x,f(x)) is also on the graph.
 Monotone functions: A function is said to be monotone if it is either decreasing or increasing. f(x) = x^{3} is a monotone function and is always increasing.
An increasing function f(x) has the property that if x_{1} > x_{2} then f(x_{1}) ≥ f(x_{2}). If f(x_{1}) > f(x_{2}) then the function is called strictly increasing. A decreasing function f(x) has the property that if x_{1} < x_{2} then f(x_{1}) ≥ f(x_{2}).If f(x_{1}) < f(x_{2}) then the function is called strictly decreasing.
 Periodic functions: A function which has the property that f(x + nI) = f(x) where n∈N and I is a fixed number. The number I is called the period of the periodic function, f. All trigonometric functions are periodic functions.
