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?

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

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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)?

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

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