### Concept (1)

In order for a function to have continuity at a certain point, several conditions including (1) the existence of the point in the domain and (2) the existence of a two-sided limit as the point approaches the limit must be met. If functions are continuous at every point in their domain, they we call these functions continuous functions. Examples of continuous functions are power functions, exponential functions and logarithmic functions.

### Sample Problems (3)

Need help with "Continuous Functions" problems? Watch expert teachers solve similar problems to develop your skills.

###### Problem 1
How to show that polynomial functions are continuous functions by checking the properties of continuous functions.
###### Problem 2
How to show that rational functions are continuous functions, and how to see when rational functions are not continuous.
###### Problem 3
How to show that compositions of continuous functions are continuous functions by checking continuity rules for the composition.