# Lesson Worksheet: Graphs of Rational Functions Mathematics

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

**Q2: **

The graph shows . A single point is marked on the graph. What are the values of the constants , , and ?

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q5: **

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.

**Q6: **

What is the -intercept of the function represented by the given graph?

- A
- B
- C
- D
- E

**Q7: **

Which of the following is the equation of the rational function graphed below?

- A
- B
- C
- D

**Q8: **

Which of the following is the equation of the rational function graphed below?

- A
- B
- C
- D

**Q9: **

Sketch a graph of the function and determine which graph represents it.

- A
- B
- C
- D

**Q10: **

Sketch the graph of the function , and then find the -intercept of .

- A
- B
- C
- D
- E

**Q11: **

Sketch a graph of the function , then find the -intercept of .

- A
- B
- C
- D
- E

**Q12: **

Sketch the graph of the function , then find the -intercept of .

- A
- B
- C
- D
- E

**Q13: **

Sketch the graph of the function , and then find the horizontal asymptote of .

- A
- B
- C
- D

Find the vertical asymptote of .

- A
- B
- C
- D

**Q14: **

Which function is represented by the graph shown?

- A
- B
- C
- D
- E

**Q15: **

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.

**Q16: **

Which function is represented in the following graph?

- A
- B
- C
- D
- E

**Q17: **

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.

**Q18: **

Which of the following graphs represents ?

- AGraph 2
- BGraph 1
- CGraph 3
- DGraph 4

**Q19: **

Which of the following graphs represents a function whose asymptotes are and ?

- AGraph 2
- BGraph 4
- CGraph 1
- DGraph 3

**Q20: **

Which function is represented by the graph shown?

- A
- B
- C
- D
- E

**Q21: **

Which of the following is the equation of the graphed function whose asymptotes are and ?

- A
- B
- C
- D
- E

**Q22: **

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

- AThe value of approaches .
- BThe value of approaches .
- CThe value of approaches 2.
- DThe value of approaches .
- EThe value of approaches 1.

**Q23: **

Which of the following represents the function whose asymptotes are the same as those of the graphed function ?

- A
- B
- C
- D
- E

**Q24: **

Consider the graph of the function .

What is the end behavior of the graph as increases along the positive ?

- AThe value of approaches .
- BThe value of approaches 2.
- CThe value of approaches .
- DThe value of approaches .

What is the end behavior of the graph as decreases along the negative ?

- AThe value of approaches 2.
- BThe value of approaches .
- CThe value of approaches .
- DThe value of approaches .

**Q25: **

Which of the following is the graph of the function ?

- A
- B
- C
- D
- E