Increasing or decreasing function

        ∀ 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.

Illustration:

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

Solution:

Since, ∀ x ε R, y ε R

        Therefore D_f = 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.