# Lesson Worksheet: Domain and Range of a Function Mathematics

In this worksheet, we will practice identifying the domain and range of functions from their equations.

**Q4: **

If , where , find the range of .

- A
- B
- C
- D

**Q7: **

Determine the range of the function in the given figure.

- A
- B
- C
- D
- E

**Q8: **

Determine the domain of the function represented in the graph below.

- A
- B
- C
- D
- E

**Q9: **

Determine the domain of the function .

- A
- B
- C
- D

**Q10: **

Determine the domain of the function .

- A
- B
- C
- D
- E

**Q11: **

Determine the range of the function represented in the figure below.

- A
- B
- C
- D

**Q13: **

Given the function , answer the following.

Evaluate .

Evaluate .

Evaluate .

- A3
- B7
- C1
- D is not defined at 0.
- E2

What is the domain of ?

- A
- B
- C
- D
- E

What is the range of ?

- A
- B
- C
- D
- E

Solve .

- A or
- B or
- C or
- D
- E or

What is the solution set of ?

- A
- B
- C
- D
- E

What is the solution set of ?

- A
- B
- C
- D
- E

**Q14: **

Determine the domain and the range of the function .

- AThe domain is , and the range is .
- BThe domain is , and the range is .
- CThe domain is , and the range is .
- DThe domain is , and the range is .
- EThe domain is , and the range is .

**Q15: **

Functions and have the same domain {1, 2, 3, 4}.
Which of the following statements *must* be true?

- The range of has at most 4 elements.
- The range of has elements, where = the size of the range of and = the size of the range of .
- The range of has at least 1 element.

- Aa only
- Ba and c
- Cb only
- Dc only

**Q16: **

What is the range of the function on the domain (which is the domain of all of the integers)?

- Aall the integers
- Ball the numbers of the form where is an integer
- CWe cannot tell the range because we do not know the codomain.
- Dall the positive integers
- Eall the rational numbers

**Q18: **

If , where , find the range of .

- A
- B
- C
- D

**Q19: **

Given that and , where the graph of the function can be represented by , determine its range.

- A
- B
- C
- D
- E

**Q20: **

, , and is a relation from to , where means that for each and . Determine the relation , state whether it represents a function or not, and write its range if it is a function.

- A, a function from to , range
- B, a function from to , range
- C, not a function from to
- D, not a function from to

**Q21: **

For two sets and , a function exists from to . Also, , , and means is a multiple of . If , , and , find the range of the function.

- A
- B
- C
- D
- E

**Q22: **

If is a function from the set to the set , which set contains the range of ?

- A
- B

**Q23: **

is a function from to , where means that is divisible by for each and . If , , and , determine the range of the function.

- A
- B
- C
- D

**Q24: **

, , is the set of natural numbers, and is a function from to where means . Given that and , write the range of the function.

- A
- B
- C
- D

**Q25: **

If , where , find the range of .

- A
- B
- C
- D
- E