Continuity Exploration

The following questions relate to continuity of a function f at an input value x = a. If you need a refresher on what it means for a function to be continuous at any input value, refer to this worksheet.

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 of the functions below is NOT continuous at x=0 because of the reason in Question 1?

f(x)= -1,

= 1, x>0

f(x)= x,

= 1, x=0

5) Which of the functions below is NOT continuous at x=0 because of the reason in Question 2?

f(x)= -1,

= 1, x>0

f(x)= x,

= 1, x=0

6) Which of the functions below is NOT continuous at x=0 because of the reason in Question 3?

f(x)= x,

= 1, x=0

f(x)= -1,

= 1, x>0

7) Which of the functions below IS continuous at x=0?

f(x)= -1,

= 1, x>0

f(x)= x,

= 1, x=0

Continuity Exploration

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 of the functions below is NOT continuous at x=0 because of the reason in Question 1?

5) Which of the functions below is NOT continuous at x=0 because of the reason in Question 2?

6) Which of the functions below is NOT continuous at x=0 because of the reason in Question 3?

7) Which of the functions below IS continuous at x=0?

Information: Continuity Exploration