# Worksheet: Rational Functions

In this worksheet, we will practice identifying, writing, and evaluating a rational function.

Q1:

The figure shows the graph of . Write down the equations of the two asymptotes of .

• A and
• B and
• C and
• D and
• E and

What is the domain of the function?

• A
• B
• C
• D
• E

What is the range of the function?

• A
• B
• C
• D
• E

Q2:

Consider the function .

By considering the point at which the denominator equals zero, find the domain of the function.

• A
• B
• C
• D
• E

To find the range of the function, a handy trick is to divide the numerator and denominator of through by . What expression does this give us?

• A
• B
• C
• D

Now, taking the limit of this expression as tends to infinity will give us the value of which is not in the range of the original function. Use this to state the range of the function.

• A
• B
• C
• D
• E

Hence, state the equations of the two asymptotes.

• A and
• B and
• C and
• D and
• E and

Q3:

The following is the graph of the triangle wave function . What is the domain of its reciprocal function ?

• Aall real numbers
• Beven integers
• Call integers
• Dall real numbers that are not integers
• Eodd integers

Q4:

Find for the function .

• A
• B
• C
• D
• E

Q5:

Simplify the function , and find the values of for which .

• A, or
• B, or
• C, or
• D, or
• E, or

Q6:

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

Q7:

Given that , where and , determine the values of and .

• A,
• B,
• C,
• D,
• E,

Q8:

The function has two asymptotes at and . Given that , determine the values of and .

• A,
• B,
• C,
• D,
• E,

Q9:

Write a rational function in the simplest form , given that the vertical asymptote is at , the horizontal asymptote is at , and .

• A
• B
• C
• D
• E