RATEY
October 22, 2013
Graph and compare asymptotes:
RATEY
October 22, 2013
Asymptotic
Behavior
No
Togetherness
ODD
Togetherness
EVEN
RATEY
October 22, 2013
What about roots? When is there a tangent root?
pass
through
roots
tangent
root
ODD
EVEN
RATEY
October 22, 2013
1 Which of the following cause the roots of a rational graph? [note: you may choose one or more than one]
A
denominator = 0
B
factor cancels out
C
numerator = 0
D
x = 0
E
y = 0
F
behavior at +∞ and -∞
RATEY
October 22, 2013
Find the roots.
RATEY
October 22, 2013
2 Which of the following cause the vertical asymptotes of a rational graph? [note: you may choose one or more than one]
A
denominator = 0
B
factor cancels out
C
numerator = 0
D
x = 0
E
y = 0
F
behavior at +∞ and -∞
RATEY
October 22, 2013
Find the vertical asymptotes.
RATEY
October 22, 2013
3 Which of the following cause a point discontinuity (hole) in a rational graph? [note: you may choose one or more than one]
A
denominator = 0
B
factor cancels out
C
numerator = 0
D
x = 0
E
y = 0
F
behavior at +∞ and -∞
RATEY
October 22, 2013
Find the points of discontinuity.
RATEY
October 22, 2013
4 Which of the following cause the end behavior of a rational graph? [note: you may choose one or more than one]
A
denominator = 0
B
factor cancels out
C
numerator = 0
D
x = 0
E
y = 0
F
behavior at +∞ and -∞
RATEY
October 22, 2013
Find the end behavior.
RATEY
October 22, 2013
5
Which of the following cause the y­intercepts of a graph? [note: you may choose one or more than one]
A
denominator = 0
B
factor cancels out
C
numerator = 0
D
x = 0
E
y = 0
F
behavior at +∞ and -∞
RATEY
October 22, 2013
Find the y­intercepts.
RATEY
October 22, 2013
Click by the rotating letter.
R
A
T
E
Y
An organizational tool for graphing rational functions:
Roots ­ when numerator = 0
RATEY
October 22, 2013
Click by the rotating letter.
R
A
T
E
Y
An organizational tool for graphing rational functions:
Roots ­ when numerator = 0
Asymptotes ­ when denominator = 0
RATEY
October 22, 2013
Click by the rotating letter.
An organizational tool for graphing rational functions:
R
Roots ­ when numerator = 0
A
Asymptotes ­ when denominator = 0
T
E
Y
Tangency = Even power in num.
Togetherness = Even power in denom.
RATEY
October 22, 2013
Click by the rotating letter.
An organizational tool for graphing rational functions:
R
Roots ­ when numerator = 0
A
Asymptotes ­ when denominator = 0
Tangency = Even power in num.
Togetherness = Even power in denom.
T
E
Y
End behavior ­ look at + ∞ and -∞
RATEY
October 22, 2013
Click by the rotating letter.
An organizational tool for graphing rational functions:
R
Roots ­ when numerator = 0
A
T
Asymptotes ­ when denominator = 0
Tangency = Even power in num.
Togetherness = Even power in denom.
E
End behavior ­ look at + ∞ and -∞
Y
y­intercepts ­ let x = 0
RATEY
October 22, 2013
Click by the rotating letter.
An organizational tool for graphing rational functions:
R
Roots ­ when numerator = 0
A
Asymptotes ­ when denominator = 0
Tangency = Even power in num.
Togetherness = Even power in denom.
T
E
Y
End behavior ­ look at + ∞ and -∞
y­intercepts ­ let x = 0
RATEY
October 22, 2013
R
A
T
E
Y
RATEY
October 22, 2013
R
A
T
E
Y
1.
RATEY
October 22, 2013
R
A
T
E
Y
2.