# Worksheet: Domain and Range of a Rational Function

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

Q1:

Find the value of given where is undefined.

• A
• B
• C
• D14
• E

Q2:

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 .

Q3:

Simplify the function , and find its domain.

• A , domain
• B , domain
• C , domain
• D , domain
• E , domain

Q4:

Find the domain of the function .

• A
• B
• C
• D

Q5:

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

• Azeros of the function
• Bzeros of the denominator of the function

Q6:

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 .

Q7:

Define a function on real numbers by .

What is the domain of this function?

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

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 .

• 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 .

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 .

• AThe domain is , the range is .
• BThe domain is , the range is .
• CThe domain is , the range is .
• DThe domain is , the range is .

Q17:

Determine the domain and the range of .

• 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 .

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 .

• 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 .

Q22:

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 .

Q23:

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 .

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 .

• 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 .