This lesson includes 21 additional questions and 205 additional question variations for subscribers.

# Lesson Worksheet: Graphs of Rational Functions Mathematics • 10th Grade

In this worksheet, we will practice graphing rational functions whose denominators are linear, determining the types of their asymptotes, and describing their end behaviors.

**Q1: **

Consider the graph of the function .

By looking at the graph and substituting a few successively larger values of into the function, what is the end behavior of the graph as increases along the positive -axis?

- AThe value of approaches infinity as increases.
- BThe value of approaches zero as the value of increases.
- CThe value of approaches negative infinity as increases.

Similarly, what is the end behavior of the graph as decreases?

- AThe value of approaches zero.
- BThe value of approaches .
- CThe value of approaches .

Finally, by interpreting the graph, what is happening to the function when the value of approaches zero?

- AThe value of approaches positive infinity when gets closer to zero from the negative direction and approaches negative infinity when gets closer to zero from the positive direction.
- BThe value of approaches negative infinity when gets closer to zero from the negative direction or from the positive direction.
- CThe value of approaches positive infinity when gets closer to zero from the negative direction or from the positive direction.
- DThe value of approaches negative infinity when gets closer to zero from the negative direction and approaches positive infinity when gets closer to zero from the positive direction.

**Q7: **

Consider the graph of the function . What happens to the function when the value of approaches ?

- AThe value of approaches when gets closer to from the negative direction or from the positive direction.
- BThe value of approaches when gets closer to from the positive direction and approaches when gets closer to from the negative direction.
- CThe value of approaches when gets closer to from the negative direction or from the positive direction.
- DThe value of approaches when gets closer to from the positive direction and approaches when gets closer to from the negative direction.

**Q8: **

Consider the graph of the function . What is the end behavior of the graph as approaches 1?

- AThe value of approaches when gets closer to 1 from the positive direction and approaches when gets closer to 1 from the negative direction.
- BThe value of approaches when gets closer to 1 from the negative direction or from the positive direction.
- CThe value of approaches when gets closer to 1 from the negative direction or from the positive direction.
- DThe value of approaches when gets closer to 1 from the positive direction and approaches when gets closer to 1 from the negative direction.

**Q9: **

Which of the following is the graph of the function ?

- A
- B
- C
- D
- E