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Increasing or Decreasing Function


The function f is said to be an increasing function in its domain D if

∀ x2 > x1 => f(x2) > f(x1); x1, x2 ε D 


However if


 ∀ x2 > x1 => f(x2) > f(x1), x1, x2 ε D                

The function 'f' is said to be strictly increasing

The function 'f' is said to be decreasing function in its domain D if

∀ x2 > x1 => f(x2) < f(x1); x1, x2 ε D


However if

∀ x2 > x1 => f(x2) < f(x1); x1, x2 ε D


Then it said to be strictly decreasing.

Strictly increasing and decreasing functions are also called Monotonic Function.


Is y = 2x + 3 increasing/decreasing function.


Since, ∀ x ε R, y ε R

Therefore Df = R

Let x2 > x1; x1, x2 ε R

        =>     2x2 > 2x1

        =>     2x2 + 3 > 2x1 + 3

        =>     f(x2) > f(x1)

        =>     y = f(x) = 2x + 3 is strictly increasing function.


1. Are the following function increasing/decreasing?

        (a)    y = x3 + 8                 (b)    y = -2x + 4
Ans.  (a) Decreasing

        (b) Strictly decreasing 

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