# Continuity

The principle idea of a continuous function is that its graph is continuous, meaning that it can be drawn without lifting the pencil from the paper.

## Continuous Function at a Point

A function f(x) is continuous at a point, x = a, if and only if it meets the following conditions:

1. The point x = a has image.

2. There is a limit of the function f(x) at x = a.

3. The value of the function at the point coincides with the limit of the function at the point.

#### Example

Study the continuity of at x =2.

f(2)= 4

### Directional Continuity

#### Left-Continuous Function

#### Right-Continuous Function

A function f(x) is continuous at a point if it is left-continuous and right-continuous at the point.

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