Rational Functions

1
Rational Functions

• Section 2.6

2
Objectives

• Determine the domain, x-intercepts, and
  y-intercepts of a rational function.
• Determine the vertical asymptotes (if any) of a
  rational function.
• Determine the horizontal asymptotes (if any) of a
  rational function.
• Determine the slant asymptotes (if any) of a
  rational function.
• Find a rational function given the vertical
  asymptotes, the horizontal asymptote, and
  x-intercepts.
• Solve a word problem involving a rational
  functions.

3
Vocabulary

• rational function
• vertical asymptote
• hole
• horizontal asymptote
• slant asymptote

4
Find the domain, x-intercepts, y-intercepts,
vertical asymptotes, and horizontal asymptotes
for
5
Find the domain, x-intercepts, y-intercepts,
vertical asymptotes, and horizontal asymptotes
for
6
Find the domain, x-intercepts, y-intercepts,
vertical asymptotes, and horizontal asymptotes
for
7
Find the rational function that has the following
conditions

• the vertical asymptotes are and
• the horizontal asymptote is
• the x-intercepts are
• and

8
In Teaneck, the fruit fly population in millions
is modeled by where t is in months after June
1, 2002. Estimate the initial population of
fruit flies on June 1, 2002. Estimate the
population after many months - for example many
years into the future
9
Find the slant asymptote for