# Continuity of Functions

### Topics

## Introduction to Continuity Of Functions - At A Glance:

It's good to have a feel for what continuity at a point looks like in pictures. However, sometimes we are asked about the continuity of a function for which we're given a formula, instead of a picture. When this happens, remember that the following three statements must **all** hold for *f* to be continuous at *c*.

- I. The function
*f*is defined at*x*=*c*.

- The limit exists.

- The value
*f*(*c*) agrees with the limit .

#### Example 1

Determine whether the function
is continuous at |

#### Example 2

Determine whether the function
is continuous at |

#### Example 3

Determine whether the function
is continuous at |

#### Example 4

Determine whether the function is continuous at |

#### Example 5

At what values is the function |

#### Exercise 1

Determine whether the function

x = -5 x = -4 x = 0 x = 2 x = 3

#### Exercise 2

For the function, determine all values at which the function is discontinuous.

#### Exercise 3

For the function, determine all values at which the function is discontinuous.

#### Exercise 4

For the function, determine all values at which the function is discontinuous.