# Continuity Exploration Assignment

- Author:
- Tim Brzezinski,

- Topic:
- Continuity

The following questions relate to

**continuity of a function f at an input value**For the definition of a function to be continuous at any input value, please refer to this worksheet first.*x*= a.## Graph for Question 1

## 1) Why is this function not continuous at x = a? (Slide the dot to change the graph.)

## Graph for Question 2

## 2) Why is this function not continuous at x = a? (Slide the dot to change the graph.)

## Graph for Question 3

## 3) Why is this function not continuous at x = a? (Slide the dots to change the graph.)

4) Which one of these functions is NOT continuous at x=0 because f(x) is not defined at x=0?

5) Which one of these functions is NOT continuous at x=0 because the limit as x->0 of f(x) does not exist?

6) Which one of these functions is NOT continuous at x=0 because the limit as x->0 of f(x) does NOT equal f(a)?

7) Which one of these functions IS continuous at x=0?