# Worksheet: Simplifying Rational Functions

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:

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

Q5:

Given that simplifies to , what is the value of ?

Q6:

Simplify the function and find its domain.

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

Q7:

Simplify the function , and find its domain.

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

Q8:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q9:

Which of the following functions are equal?

• A ,
• B ,
• C ,
• D ,
• E ,

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:

Which of the following functions are equal?

• A ,
• B ,
• C ,
• D ,
• E ,

Q13:

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

Q14:

Simplify the function , and find its domain.

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

Q15:

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

• A
• B
• C
• D
• E

Q16:

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

Q17:

Determine the domain of the function .

• A
• B
• C
• D
• E

Q18:

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

• A
• B
• C
• D
• E

Q19:

Given that , , and , find if possible.

• A
• B4
• C
• D
• E64

Q20:

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

• A
• B
• C
• D
• E

Q21:

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

• A
• B
• C
• D
• E

Q22:

Simplify the function , and find its domain.

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

Q23:

Simplify the function , and find its domain.

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

Q24:

Simplify the function , and find its domain.

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

Q25:

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

• A
• B the domain of the domain of
• C the domain of the domain of and
• Dthe domain of the domain of and for each in the common domain