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.

Continuity

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.

Continuous Function at a Point

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

Continuous Function at a Point

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

Continuous Function at a Point

Example

Study the continuity of Continuous Function at a Point at x =2.

f(2)= 4

Continuity Operations

Continuity Operations

gráfica continua



Directional Continuity

Left-Continuous Function

Right-Continuous Function

Left-Continuous Function

Left-Continuous Function


Right-Continuous Function

Left-Continuous Function

Right-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.

Continuous Function

Continuous Function

Continuous Function