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 .

A

B

C

D

E

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 .

A

B

C

D

E

Q7:

Find the domain of the function .

A

B

C

D

Q8:

Find the domain of the function .

A

B

C

D

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 .