Post on 04-Jan-2016
description
2.6 Rational Functions2.6 Rational Functions
Asymptotes;Asymptotes;
Can’t touch this stuffCan’t touch this stuff
Asymptote
as·ymp·tote /ˈasəm(p)ˌtōt/
Noun: A line that continually approaches a given curve but does not meet it at any finite distance.
Math wants to know the behavior of the function coming at it from the Right or Left.
x is all real numbers but what value in the function 1
1)(
x
xxf
x is all real numbers except what value in the function
x ≠ 1 The asymptotes would be x = 11
1)(
x
xxf
x is all real numbers except what value in the function
x ≠ 1 The asymptotes would be x = 11
1)(
x
xxf
x is all real numbers except what value in the function
x ≠ 1 The asymptotes would be x = 1
Vertical asymptotes
is 1
Since the you
can not have zero
in the denominator.
1
1)(
x
xxf
x is all real numbers but what value in the function
x ≠ 1 The asymptotes would be x = 1
Horizontal
asymptotes
Is also 1
1
1)(
x
xxf
To find the Horizontal Asymptote
Look the equation
If n = m, then the horizontal asymptote is
If n < m, then the horizontal asymptote is 0.
If n > m, then No horizontal asymptote
If n = m + 1, then we have a slant asymptote.
Slant asymptote is y =
dcx
baxm
n
c
ay
dcxbax mn )(
Behavior as the function approaches the asymptote
Behavior as the function approaches the asymptote
From the Right
From the Left
Also,
1,)( xxf
1,)( xxf
xxf
xxf
,1)(
,1)(
Lets graph
2
222
x
xx
Homework
Page 174 – 177
# 5, 9, 17, 27,
45, 53, 69, 73,
91
HomeworkHomework
Page 174 – 177Page 174 – 177
## 7, 11, 19, 37, 7, 11, 19, 37,
49, 57, 71, 8749, 57, 71, 87