# Worksheet: Classifying Discontinuities

In this worksheet, we will practice differentiating between the three types of function discontinuity at a given point.

**Q1: **

Consider the function

What is ?

What is ?

What is ?

What type of discontinuity does the function have at ?

- AThe function has an essential discontinuity at .
- BThe function has a jump discontinuity at .
- CThe function does not have a discontinuity at .
- DThe function has a removable discontinuity at .

**Q2: **

Consider the function

What is ?

What is ?

- A1
- B0
- CThe limit does not exist.
- D
- E

What is ?

- A
- BThe limit does not exist.
- C0
- D1
- E

What type of discontinuity does the function have at ?

- AThe function does not have a discontinuity at .
- BThe function has an essential discontinuity at .
- CThe function has a removable discontinuity at .
- DThe function has a jump discontinuity at .

**Q3: **

Consider the function . Find the type of discontinuity that the function has at , if it has any.

- AThe function has a removable discontinuity at .
- BThe function does not have a discontinuity at .
- CThe function has a jump discontinuity at .
- DThe function has an infinite discontinuity at .

**Q4: **

Consider the function Find the type of discontinuity that the function has at , if it has any.

- AThe function has a jump discontinuity at .
- BThe function has a removable discontinuity at .
- CThe function does not have a discontinuity at .
- DThe function has an infinite discontinuity at .

**Q5: **

Consider the function .

Find the type of discontinuity that the function has at , if it has any.

- AThe function has a removable discontinuity at .
- BThe function has a jump discontinuity at .
- CThe function has an infinite discontinuity at .
- DThe function does not have a discontinuity at .

**Q6: **

Consider the graph of the function shown.

Find the type of discontinuity that the function has at , if it has any.

- AThe function has a removable discontinuity at .
- BThe function has a jump discontinuity at .
- CThe function does not have a discontinuity at .
- DThe function has an infinite discontinuity at .

Find the type of discontinuity that the function has at , if it has any.

- AThe function has a jump discontinuity at .
- BThe function has a removable discontinuity at .
- CThe function does not have a discontinuity at .
- DThe function has an infinite discontinuity at .

Find the type of discontinuity that the function has at , if it has any.

- AThe function has a removable discontinuity at .
- BThe function has a jump discontinuity at .
- CThe function has an infinite discontinuity at .
- DThe function does not have a discontinuity at .

Find the type of discontinuity that the function has at , if it has any.

- AThe function has a jump discontinuity at .
- BThe function has a removable discontinuity at .
- CThe function has an infinite discontinuity at .
- DThe function does not have a discontinuity at .

**Q7: **

Consider the function Find the type of discontinuity that the function has at , if it has any.

- AThe function has a jump discontinuity at .
- BThe function has an infinite discontinuity at .
- CThe function does not have a discontinuity at .
- DThe function has a removable discontinuity at .

**Q8: **

Consider the function . Find the type of discontinuity that the function has at , if it has any.

- AThe function has an infinite discontinuity at .
- BThe function does not have a discontinuity at .
- CThe function has a jump discontinuity at .
- DThe function has a removable discontinuity at .

**Q9: **

Consider the function . Find the type of discontinuity that the function has at , if it has any.

- AThe function does not have a discontinuity at .
- BThe function has a jump discontinuity at .
- CThe function has an infinite discontinuity at .
- DThe function has a removable discontinuity at .

**Q10: **

Consider the function .

Find the type of discontinuity that the function has at , if it has any.

- AThe function has a removable discontinuity at .
- BThe function has a jump discontinuity at .
- CThe function has an infinite discontinuity at .
- DThe function does not have a discontinuity at .

Find the type of discontinuity that the function has at , if it has any.

- AThe function has an infinite discontinuity at .
- BThe function does not have a discontinuity at .
- CThe function has a removable discontinuity at .
- DThe function has a jump discontinuity at .

**Q11: **

Consider the function . Find the type of discontinuity that the function has at , if it has any.

- AThe function does not have a discontinuity at .
- BThe function has a removable discontinuity at .
- CThe function has an infinite discontinuity at .
- DThe function has a jump discontinuity at .

**Q12: **

Consider the function . Find the type of discontinuity that the function has at , if it has any.

- AThe function has a jump discontinuity at .
- BThe function does not have a discontinuity at .
- CThe function has an infinite discontinuity at .
- DThe function has a removable discontinuity at .

**Q13: **

Consider the function What type of discontinuity does the function have at , if it has any?

- AThe function does not have a discontinuity at .
- BThe function has a removable discontinuity at .
- CThe function has a jump discontinuity at .
- DThe function has an infinite discontinuity at .

**Q14: **

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

- AThe function is already continuous at .
- B makes continuous at .
- CThe function cannot be made continuous at because is undefined.
- DNo value of will make continuous because does not exist.

**Q15: **

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

- AThe function is already continuous at .
- B makes continuous at .
- CNo value of will make continuous because does not exist.
- DThe function cannot be made continuous at because is undefined.

**Q16: **

Suppose If possible, define so that is continuous at .

- AThe function is already continuous at .
- B would make continuous at .
- C would make continuous at .
- DThe function can not be made continuous at because does not exist.

**Q17: **

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

- AThe function is already continuous at .
- B would make continuous at .
- C would make continuous at
- DThe function can not be made continuous at because does not exist.

**Q18: **

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

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