# Continuity of a function(continuous and discontinuous functions).

A function “f” in interval [a,b] is said to be a **continuous** **function** when the Graph drawn for f(x) is a smooth line or curve without any break in it.

Such curve or line can be drawn by the continuous motion of a pencil in a sheet of paper.

And **Discontinuous function **is just opposite of the continuous function , the function “f” is said to be discontinuous function when the graph drawn for f(x) is consists of disconnected curves or lines.

For example:

Continuous Function:

Discontinuous Function:

If we zoom into the disconnected place of two curves it looks like:

When x_{a} is any point in the interval [a,b] then the following relation should be true in the curve for the function “f” to be a continuous function if the following relation is not true in the curve then it is a discontinuous function.

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