Strictly increasing and decreasing functions

Let 'f ' be a real function on an interval I.
Then 'f' is said to be a

(i) Strictly increasing function on I if x1 < x2
⇒ f(x1) < f(x2) ∀ x1, x2 ∈ I      
i.e., f(x) increases as 'x' increases.

(ii) Strictly decreasing function on I if x1 < x2
⇒ f(x1) > f(x2) ∀ x1, x2 ∈ I    
i.e, f(x) decreases as 'x' increases.

Graphically, a function 'f ' is

(i) strictly increasing on [a, b] if as x moves to right hand side values from x = a to x = b, [a, b]
its graph moves upwards as shown in fig (i).

(ii) strictly decreasing on [a, b] if as x moves to right hand side values from x = a to x = b, [a, b]
its graph moves downwards as shown in fig (ii).

For important points to remember click