Increasing function

Definition
In an Increasing function, as the value of $x$ increases the value of $y$ increases.

Let $f$ be a real valued function and $I \subseteq \mathbb{R}$ be the domain, then $f$ is said to be:

• Increasing on $I$ if for all $x_1,x_2\in I:x_1<x_2\Rightarrow f(x_1)\le f(x_2)$ .
• Strictly increasing on $I$ if for all $x_1,x_2\in I:x_1<x_2\Rightarrow f(x_1)<f(x_2)$ .

Explanation

Consider the graph on the right side of the page. Observe that as we move from left to right along the graph, the height of the graph continuously increases. For this reason, the function is said to be increasing for all real numbers $x \in \R$ .