Rational Functions
If power of numerator = power of denominator
Horizontal Asymptote is y = C (the ratio of the leading coefficients )
If power of numerator < power of denominator
Horizontal asymptote is at y = 0
If power of numerator > power of denominator
Oblique/Slant Asymptote
When a zero/factor is in the numerator and denominator
Removable Discontinuity
Used to determine the equation of an oblique asymptote
Synthetic/Long Division
Values that are not a part of the domain because they make the denominator zero
Vertical Asymptotes
y = 3
What are the horizontal asymptote?
(-3,0); (1,0)
What are the x-intercepts?
(2,0)
What are the x-intercepts?
(3,0)(-4,0)
What are the x-intercepts?
(4, 0)
What are the x-intercepts?
none
What are the x-intercepts?
x ≠ -2
What is the domain?
x≠0; x≠3
What is the domain?
none
What is the horizontal asymptote?
y = 0
What is the horizontal asymptote??
(0, -1/6)
What is the y-intercept?
(0, 0)
What is the y-intercept?
none
What is the y-intercept?
x=-1; x=3
What is/are the vertical asymptote(s)?
x=3
What is/are the vertical asymptote(s)?
x=3; x=-3
What is/are the vertical asymptote(s)?
Vertical Asymptote at x= 4 and a hole when x = -3
a
Horizontal Asymptote at y=3 and Vertical Asymptote at x = 4
b
Vertical Asymptote at x = 2, hole when x = 1
c
Hole when x = -1, Vertical Asymptote at x = 1
d
Horizontal Asymptote y=0 and a Vertical Asymptote at x = 0
e
Horizontal Asymptote at y=0 and 3 points of discontinuity
f
Vertical Asymptote at x = -3 and x=4
g
Hole at x=0 and 1 other point of discontinuity.
h
No vertical Asymptote
i
Vertical Asymptote at x = 5
j
No horizontal Asymptote and hole at x =4
k
Horizontal Asymptotes at y=1 and y=-1
l
Set the numerator equal to zero
x - intercepts
Substitute x = 0 into the function
y - intercept
