# What is a continuous function?

##### 1 Answer

A continuous function is a function that is continuous at every point in its domain.

That is

#### Explanation:

We normally describe a continuous function as one whose graph can be drawn without any jumps. That's a good place to start, but is misleading.

An example of a well behaved continuous function would be

graph{x^3-x [-2.5, 2.5, -1.25, 1.25]}

In fact any polynomial is well defined everywhere and continuous.

A less obvious example of a continuous function is

graph{tan(x) [-10, 10, -5, 5]}

This appears to be discontinuous, with 'jumps' at

Similarly, the following function is continuous on its domain

graph{x/abs(x) [-5, 5, -2.5, 2.5]}

If we add a definition of

graph{(y-x/abs(x))(x^2+y^2-0.002) = 0 [-5, 5, -2.5, 2.5]}

This