In this worksheet, we will practice finding the domain and range of a rational function either from its graph or its defining rule.

**Q3: **

Simplify the function , and find its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q5: **

The domain of an algebraic fractional function is the set of all real numbers except the .

- A zeros of the denominator of the function
- B zeros of the function

**Q6: **

Determine the domain and the range of the function .

- A The domain is and the range is .
- B The domain is and the range is .
- C The domain is and the range is .
- D The domain is and the range is .
- E The domain is and the range is .

**Q7: **

Define a function on real numbers by .

What is the domain of this function?

- Aall real numbers
- Ball real numbers except
- Call real numbers except
- Dall real numbers except
- Eall real numbers except

Find the one value that cannot take.

- A
- B
- C
- D
- E

What is the range of this function?

- Aall real numbers except
- Ball real numbers
- Call real numbers except
- Dall real numbers except
- Eall real numbers except

**Q8: **

Given that the domain of the function is , evaluate .

**Q9: **

Determine the domain and the range of the function .

- A The domain is and the range is .
- B The domain is and the range is .
- C The domain is and the range is .
- D The domain is and the range is .

**Q10: **

Identify the domain of .

- A
- B
- C
- D
- E

**Q11: **

Determine the domain of the function .

- A
- B
- C
- D
- E

**Q12: **

For which values of is the function not defined?

- A
- B
- C
- D
- E

**Q13: **

If the common domain of the two functions and is , what is the value of ?

**Q14: **

The function has an additive inverse if the domain is .

- A
- B
- C
- D
- E

**Q15: **

If the function , what is the domain of its multiplicative inverse?

- A
- B
- C
- D

**Q16: **

Determine the domain and the range of the function .

- A The domain is , the range is .
- B The domain is , the range is .
- C The domain is , the range is .
- D The domain is , the range is .

**Q17: **

Determine the domain and the range of .

- A The domain is and the range is .
- B The domain is and the range is .
- C The domain is and the range is .
- D The domain is and the range is .
- E The domain is and the range is .

**Q18: **

Determine the domain of the function .

- A
- B
- C
- D

**Q19: **

Given the function , find the multiplicative inverse of in its simplest form and state its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q20: **

Determine the domain of the function .

- A
- B
- C
- D

**Q21: **

Determine the domain and the range of the function .

- A The domain is and the range is .
- B The domain is and the range is .
- C The domain is and the range is .
- D The domain is and the range is .

**Q22: **

Determine the domain and the range of the function .

- A The domain is , and the range is .
- B The domain is , and the range is .
- C The domain is , and the range is .
- D The domain is , and the range is .
- E The domain is , and the range is .

**Q23: **

Determine the domain and the range of the function .

- A The domain is and the range is .
- B The domain is and the range is .
- C The domain is and the range is .
- D The domain is and the range is .

**Q24: **

Given that the domain of the function is the same as the domain of the function , what is the value of ?

**Q25: **

Determine the domain and the range of the function .

- A The domain is and the range is .
- B The domain is and the range is .
- C The domain is and the range is .
- D The domain is and the range is .
- E The domain is and the range is .