Types of functions

  • Even and odd functions: A function f(x) is said to be an even function if f(-x) = f(x), f(x) = x2 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 = x3 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) = x3 is a monotone function and is always increasing.
    An increasing function f(x) has the property that if x1 > x2 then f(x1) ≥ f(x2). If f(x1) > f(x2) then the function is called strictly increasing.
    A decreasing function f(x) has the property that if x1 < x2 then f(x1) ≥ f(x2).If f(x1) < f(x2) 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.





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