Monotonocity of function

Let y = f (x) be a given function with ‘ D ‘ as it’s domain. Let D1 ⊆ D then;

Increasing Function:

f(x) is said to be increasing in D1 if for every x1 , x2 ∈ D1, x1 > x2 ⇒ f(x1) > f (x2)

It means that there is a certain increase in the value of f (x) with an increase in the value of x. Refer to fig.2

Non-Decreasing Function:

f (x) is said to be non-decreasing in D1 if for every x1 , x2 ∈ D1 , x1 > x2

⇒ f(x1) ≥ f (x2 ). It means that the value of f (x) would never decrease with an increase in the value of x. Refer to fig.

Decreasing Function:

f(x) is said to be decreasing in D1 if for every x1, x2 ∈ D1, x1 > x2

⇒  f (x1) < f (x2 It means that there is a certain decrease in the value of f (x) with an increase in the value of x. Refer to fig.

Non-Increasing Function:

f (x) is said to be non-increasing in D1 if for every x1, x2 ∈ D1, x1 > x2

=> f (x1) ≤ f (x2 ). It means that the value of f (x) would never increase with an increase in the value of x.Refer to fig.

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