Question

What is a continuous function?

Answer 1

Hint: Here we have to define what is a continuous function . Firstly we will write the basic definition of continuity. Then we will explain what a continuous function is and what are the properties that a function should satisfy in order to be continuous. Finally we will give some tricks to find which function is continuous.

Complete answer:
Firstly we will define what continuity is.
Continuity of any function states the characteristics of the function and its functional value.
A function is said to be continuous if it satisfies the following properties.
Let us take any function $f\left( x \right)$ so at a point $x=a$ present in the domain of the function the three conditions should be satisfied:
 1. Value of $f\left( a \right)$ is finite which means it should exist.
2. $$\displaystyle \lim_{x \to a}$$ f(x) Exist which means both Left hand Limit and Right hand limit should be finite and equal.
3. $$\displaystyle \lim_{x \to a}$$f(x)=f(a) then the function $f\left( x \right)$ is continuous at $x=a$ .
A simple method to find whether a function is continuous or not is that the graph of the function should be an unbroken curve.
Example: f(x)=x, f(x)=1 etc are continuous functions.

Note:
Many functions have a property that we can draw their graph without lifting your pencil from the paper surface. This type of function is known as continuous function. Even if from the given three properties one property is not satisfied our function becomes discontinuous at the given point.