Misc.
X-intercepts
Y-intercepts
Vertical Asymptotes
Horizontal Asymptotes
100

When finding the HA, y=o when...

The degree is bigger on the bottom (Bottom Heavy)

100

X-int of the function x-2/x-4

(2,0)

100
The y-int of the function x^2-x-6/x^2-1
(0,6)
100
The VA of the function x^3/x^2-9
x=2
100
The HA of the function f(x)=x-2/x-4
y=1
200

How do you find the VA

Excluded Values remaining after simplifying (EV that aren't holes)

200

X-int of the function x-1/x^2-x-6

(1,0)

200
The y-int of the function x-1/x^2-x-6
(0,1/6)
200
The VA of the function 2(x+3)(x-3)/(x+1)(x+5)
x=-1 x=-5
200
The HA of the function x^3/x^2-9
y=none
300

y = leading coefficients divided by each other  when...

The degree is equal on the top and bottom of the equation

300
X-int of the function 2x+3/3x^2+7x-6
(-3,0) (2/3,0)
300

The y-int of the function x^2-4/x^2(x-3)

(-2,0) (2,0)

300
The VA of the function x^2-x-2/x-2
x=none
300
The HA to the function 2(x+3)(x-3)/(x+1)(x+5)
y=2
400

The HA does not exist when...

The degree is bigger on top (Top Heavy)

400
X-int of the function x-1/(x-2)(x+3)
(1,0)
400
The y-int of the function 2(x+3)(x-3)/(x+1)(x+5)
(0,-18/5)
400
The VA of the function x^3+x^2-6x/4x^2+4x-8
x=none
400
The HA to the function 1/3x^2+3x-18
y=none
500

How do you find the slant asymptote?

Divide the top by the bottom. The answer without the remainder is the slant asymptote. Synthetic Division

500
X-int of the function 1/3x^2+3x-18
None
500
The y-int of the function x-1/(x-2)(x+3)
(0,1/6)
500
The VA of the function x-2/x-4
x=4
500
The HA of the function x^2-4/x^2(x-3)
y=0
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