Worksheet: Finding the Domain and Range of Rational Functions

Practice finding the domain and range of a rational function from its graph or from its defining rule. This worksheet includes questions where the numerator and denominator of the rational function have factors in common.

Q1:

Simplify the function , and find its domain.

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

Q2:

Simplify the function , and find its domain.

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

Q3:

Simplify the function , and find its domain.

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

Q4:

Identify the domain of .

Q5:

Simplify the function , and determine its domain.

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

Q6:

Determine the domain of the function .

Q7:

Find the domain of the function .

Q8:

Find the domain of the function .

Q9:

Determine the domain and the range of the function represented in the shown figure.

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 .

Q10:

Determine the domain and the range of the function represented in the shown figure.

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 .

Q11:

Find the domain and 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 .

Q12:

Determine the domain and the range of the function in .