1. 23 – Limits and Continuity I – Day 2 No Calculator
Piecewise Investigations
23 – Limits and Continuity I – Day 2 No Calculator

2. This is the graph of f(x).
f(x) is continuous at x = a if and only if all three of the following are true:
1. Is f continuous at x = 6?
A. f(6) exists
Yes…f continuous at x = 6
This is the graph of f(x).

3. This is the graph of f(x).
f(x) is continuous at x = a if and only if all three of the following are true:
2. Is f continuous at x = –2?
A. f(–2) exists
No…f is not continuous at x = –2
This is the graph of f(x).
this indicates a jump discontinuity.

4. This is the graph of f(x).
f(x) is continuous at x = a if and only if all three of the following are true:
3. Is f continuous at x = 0?
A. f(0) exists
Yes…f is continuous at x = 0.
This is the graph of f(x).

5. This is the graph of f(x).
f(x) is continuous at x = a if and only if all three of the following are true:
4. Is f continuous at x = 6?
A. f(6) does not exist.
f is not continuous at x = 6.
this indicates a point discontinuity.
This is the graph of f(x).

6. This is the graph of f(x).
5. Is f continuous at x = –4? If not, state the type of discontinuity.
A. f(–4) exists.
No. There is a jump discontinuity at x = –6.
This is the graph of f(x).

7. This is the graph of f(x).
6. Is f continuous at x = 0? If not, state the type of discontinuity.
A. f(0) exists.
f is continuous at x = 6.
This is the graph of f(x).

8. This is the graph of f(x).
7. Is f continuous at x = 2? If not, state the type of discontinuity.
A. f(2) does not exist.
No. There is a point discontinuity at x = 2.
This is the graph of f(x).

9. 8. Is f continuous at x = –4? If not, state the type of discontinuity.
A. f(–4) exists.
f is continuous at x = –4.

10. 9. Is f continuous at x = 2? If not, state the type of discontinuity.
A. f(2) exists.
f is continuous at x = 2.

11. 10. Is f continuous at x = 4? If not, state the type of discontinuity.
A. f(4) exists.
f is continuous at x = 4.

12. 11. Is f continuous at x = –4? If not, state the type of discontinuity.
A. f(–4) exists.
No. A jump discontinuity exists at x = –4.

13. 12. Is f continuous at x = 2? If not, state the type of discontinuity.
A. f(2) does not exist.
No. A point discontinuity exists at x = 2.

14. 13. Is f continuous at x = 5? If not, state the type of discontinuity.
A. f(5) exists.
No. A jump discontinuity exists at x = 5.