Written Assignment #10: Rational Functions

1. (Standard 10) Consider the following rational function

a. Write the domain of r(x)in interval notation

b. Find the discontinuities of r(x)and label each as a hole or a

vertical asymptote.

c. Explain how you decide if there is a hole or a vertical asymptote.

d. What terms in r(x)determine the end-behavior? Describe the

end-behavior of r(x), using limit notation.

e. If there is a horizontal asymptote, write the equation of the

horizontal asymptote

f. Find the x- and y-intercepts of r(x)

2 a. On the graph above, label the x and y-intercepts, the holes and

the vertical asymptotes. Be sure to use equation of lines for the

vertical asymptotes. (You do NOT need to print this, but if you

don't, please write everything down or trace the graph and draw

everything in)

b. Write the limits which describe the end-behavior of the graph

using proper notation.

c. For each vertical asymptote, write down the two limits that

describe the graph of the function near that asymptote using

proper limit notation.