# Worksheet: Simplifying Rational Functions

In this worksheet, we will practice simplifying rational functions and finding their domains.

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:

Given the function , evaluate .

• A
• B
• C
• D

Q4:

Simplify the function , and find its domain.

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

Q5:

Given that and , find the largest set on which the functions and are equal.

• A
• B
• C
• D
• E

Q6:

Given the functions and , what is the set of values on which ?

• A
• B
• C
• D
• E

Q7:

Which of the following statements describes when two functions and are equal?

• Athe domain of the domain of and for each in the common domain
• B
• Cthe domain of the domain of
• Dthe domain of the domain of and

Q8:

Simplify the function and find its domain.

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

Q9:

Simplify the function and find its domain.

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

Q10:

Simplify the function , and find its domain.

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

Q11:

Simplify the function , and find its domain.

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

Q12:

Simplify the function , and find its domain.

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

Q13:

Given that the algebraic fraction simplifies to , what is the value of ?

Q14:

Given that , , and , find if possible.

• A
• B
• C
• D64
• E4

Q15:

Given that simplifies to , what is the value of ?

Q16:

Simplify the function , and find its domain.

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

Q17:

Given that the functions and are equal, what are the values of and ?

• A,
• B,
• C,
• D,
• E,

Q18:

Which of the following functions are equal?

• A,
• B,
• C,
• D,
• E,

Q19:

Simplify the function and find its domain.

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

Q20:

Which of the following functions are equal?

• A,
• B,
• C,
• D,
• E,

Q21:

Given that , and the multiplicative inverse of is , what is the value of ?

Q22:

Given the functions and , what is the set of values on which ?

• A
• B
• C
• D
• E

Q23:

Given that the multiplicative inverse of the function is , find the value of .

Q24:

Determine the domain of the function .

• A
• B
• C
• D
• E

Q25:

Simplify the function and find its domain.

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