Continuous and Discontinuous Functions Worksheet
Continuous and Discontinuous Functions Worksheet 2/15/2013
Name ____________
Process:
▪ Note where the function could have a discontinuity. This is “c”.
▪ Calculate the right side and left side limits using the correct notation and compare those limits.
▪ If the limits match then the general limit exists.
▪ Calculate f(c).
▪ If the general limit and f(c) are the same then the function is continuous at c.
Do the following questions. The first one is done for you. Read it carefully.
1. [pic]
In this case, c = 2. This is where the discontinuity could occur.
Now, find the left and right side limits.
LEFT SIDE: [pic]= 1 RIGHT SIDE: [pic]= 2
f(2) is the place where the function = 2 so sub 2 into that position: f(2) = [pic]
Now since the left and right side limits do not match, the function is discontinuous at x = 2.
2. [pic]
3. [pic]
4. [pic]
5. [pic]
6. [pic]
7. [pic]
8. [pic]
9. [pic]
10. [pic]
11. [pic]
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