# Worksheet: Continuity of a Function

In this worksheet, we will practice determining the continuity of a function at a point on the number line by evaluating limits at that point.

**Q2: **

Find the set on which is continuous.

- A is continuous on .
- B is continuous on .
- C is continuous on .
- D is continuous on .
- E is continuous on .

**Q3: **

Discuss the continuity of the function on .

- AThe function is continuous on .
- BThe function is discontinuous on .
- CThe function is continuous on .
- DThe function is continuous on .
- EThe function is continuous on .

**Q5: **

Discuss the continuity of the function at , given that

- A The function is discontinuous at because is undefined.
- B The function is discontinuous at because does not exist.
- C The function is discontinuous at because .
- D The function is continuous at .
- E The function is continuous at all points in .

**Q6: **

Let What can be said of the continuity of at ?

- A The function is discontinuous at because does not exist.
- B The function is discontinuous at because is undefined.
- C The function is discontinuous at because .
- D The function is continuous at .

**Q9: **

Find the set of values of for which the function given by is continuous.

- A
- B
- C
- D

**Q10: **

Find the set on which is continuous.

- A is continuous on .
- B is continuous on .
- C is continuous on .
- D is continuous on .

**Q11: **

Use continuity to evaluate .

- A2
- B0
- C
- D
- E6

**Q12: **

Find the set on which is continuous.

- AThe function is continuous on .
- BThe function is continuous on .
- CThe function is continuous on .
- DThe function is continuous on .
- EThe function is continuous on because and are continuous on .

**Q13: **

Given that and are continuous functions such that and , determine .

- A
- B
- C5
- D
- E

**Q14: **

Which of the following holds for ?

- A The function is continuous on because is continuous on .
- B The function is continuous on because is continuous on .
- C The function is continuous on .
- D The function is continuous on because both of and are continuous on .
- E The function is continuous on .

**Q15: **

Use continuity to evaluate .

- A
- B
- C
- D
- E8

**Q16: **

Use continuity to evaluate .

**Q17: **

Use continuity to evaluate .

- A
- B
- C55
- D

**Q18: **

Determine the value of that makes the function continuous at , given

- A
- B
- C1
- D

**Q19: **

Suppose What can be said of the continuity of at ?

- A The function is discontinuous at because does not exist.
- B The function is continuous on .
- C The function is discontinuous at because is undefined.
- D The function is continuous at .
- E The function is discontinuous at because .

**Q20: **

Given , if possible or necessary, define so that is continuous at .

- ANo value of will make continuous because does not exist.
- BThe function is already continuous at .
- CThe function cannot be made continuous at because is undefined.
- D makes continuous at .

**Q21: **

Suppose Discuss whether it is possible to define to obtain a function that is continuous at this point.

- AThe function is continuous at .
- BThe function can be defined to be continuous at as
- CThe function cannot be defined to be continuous at because does not exist.
- DThe function can be defined to be continuous at as
- EThe function cannot be defined to be continuous at because is undefined.

**Q22: **

Determine whether the function represented by the graph is continuous or discontinuous.

- Acontinuous
- Bdiscontinuous

**Q23: **

Given , what can be said of the continuity of at ?

- AThe function is discontinuous at because does not exist.
- BThe function is continuous on .
- CThe function is discontinuous at because is undefined.
- DThe function is continuous at .
- EThe function is discontinuous at because

**Q24: **

Find the set on which is continuous.

- A is continuous on because is continuous on .
- B is continuous on .
- C is continuous on because is continuous on .
- D is continuous on because and are continuous on .

**Q25: **

Discuss the continuity of the function at .

- A The function is discontinuous at because does not exist.
- B The function is continuous on .
- C The function is discontinuous at because is undefined.
- D The function is continuous at .
- E The function is discontinuous at because .