Continuity Exploration Assignment
The following questions relate to continuity of a function f at an input value x = a.
For the definition of a function to be continuous at any input value, please refer to this worksheet first.
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?