# 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.

Q2:

Which of the following graphs represents ? • A(d)
• B(a)
• C(b)
• D(c)

Q3:

What function is represented in the figure below? • A
• B
• C
• D

Q4:

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:

The graph shows . We can see that the intersection of its asymptotes is at and that the points and are below and above the graph respectively. Determine the interval in which lies. • A
• B
• C
• D
• E

Q6:

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

• A
• B
• C
• D
• E

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

Q10:

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