Find the Domain
Horizontal Asymptotes
Vertical Asymptotes
Holes
Oblique Asymptotes
100
How do you find the domain?
Set the denominator = 0
BEFORE YOU SIMPLIFY
100
How do you find the Horizontal Asymptote?
Look at the leading terms of the numerator and denominator and figure out which of the three cases you're in
100
How do you find a vertical asymptote?
Set the denominator = 0
AFTER YOU SIMPLIFY
100
What is the film this image is from?
Holes
100
How do you know if a rational function has an oblique asymptote?
The numerator has a larger degree than the denominator by exactly one.
200
Find the domain:
y=1/x
x ne 0
200
Find the HA:
(x^2-x-1)/(x^10
y=0
200
Find any VA's:
1/((x-1)(x+2)
x=1 and x=-2
200
How can you tell if a rational function has a hole?
There will be canceled out terms that simplify. That term's x-value is the location of the hole.
200
Find the oblique asymptote:
(2x^2-5x+1)/(x-1)
y=2x-3
300
Find the domain:
1/(x^2-5x-36
x ne 9 and x ne -4
300
Find the HA:
((2x-1)(x+3))/((-x-1)(x+1))
y=-2
300
Find any VA's:
(x-3)/(x^2-4x+3
x=1
300
Find any holes:
((x-1)(x+2)(x-3))/((x^2-5x+6)
x=3
300
Find the oblique asymptote:
(-3x^3+x^2+x-5)/(x^2
y=-3x+1
400
Find the domain:
(x-2)/(x^2+1
all real numbers
400
Find the HA:
(x^n)/(x^(n+2)
y=0
400
Find any VA's:
(-4(x-3))/((x+1)(x^2-9)
x=-1 and x=-3
400
Find any holes:
(x^2-10x+16)/(x^2-9)
No Holes
400
Find the oblique asymptote:
(x^3-2x^2+x-15)/(2x^2+4x-2
y=1/2x-2
500
Find the domain:
sqrt(3x-5
x geq 5/3
500
Find the HA:
(5x^4-2x^2+2x^4)/(x-1)^4
y=7
500
Find any VA's:
(x-2)/(x^2+1
None! (Denominator never = 0)
500
Find the coordinate (both x and y) of the hole:
((x-1)(x+2)(x-3))/(x(x^2-4))
Hole at (-2, 15/8)
in decimals (-2, 1.875)
500
Does the function cross its oblique asymptote? If so, where?
(x^3+x^2+3x+2)/(x^2)
Yes!
(-2/3, 1/3)