Activity 10 - Activity 10 2.7 Rational Functions Name...

Activity 10
Name
2.7 Rational Functions
Vertical Asymptotes occur where the denominator of a reduced rational function is 0.
1. Find the vertical asymptotes of f ( x ) =
x +2
( x - 2) x
: Asymptotes at x = 2 and x = 0
2. Find the vertical asymptotes of f ( x ) =
2 x
2
+2 x - 5
x 2 - 1
:
3. Find the vertical asymptotes of f ( x ) =
2 x
3
+2
( x - 2) x
:
4. Find the vertical asymptotes of f ( x ) =
( x +2)( x - 3)
x 3 - x
:
Horizontal Asymptotes may occur in a rational function f ( x ) =
a
n
x
n
+ a
n - 1
x
n - 1
+ ··· + a
0
b
m
x m + b
m - 1
x m - 1 + ··· + b
0
. If
n > m , there are no horizontal asymptotes (the function goes to ±∞ as x → ∞ ) If n = m ,
there is an asymptote at a
n
b
m
. If n < m , there is an asymptote at 0.
1. Find the horizonal asymptotes of f ( x ) = x +2
( x - 2) x
: top degree =1, bottom degree=2 ⇒
asymptote at 0
2. Find the horizonal asymptotes of f