Rational Functions

Misc.

100

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

The degree is bigger on the bottom

200

How do you find the VA

Factoring the bottom of the equation

300

To find the horizontal asymptote, coefficients are divided when...

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

400

When finding the HA, y=none when...

The degree is bigger on top

500

What is the horizontal asymptote of 

f(x)=(-x² +2x-4)/ (3x²-4)

y=-1/3

Zeros

100

Zeros of the function (x-2)/(x-4)

x=2

200

Zeros of the function (x-1)/(x²-x-6)

x=1

300

 Zeros of the function (2x+3)/(3x²+7x-6)

x=-3/2

400

Zeros of the function (x²-2x-3)/(x+3)

x=-1,3

500

Zeros of the function (x²-x-20)/(x-5)

x=-4

Holes

100

Holes of the function (x+3)/(x-3)

None

200

Holes of the function (x-7)(x+2)/(x-7)

(7,9)

300

Holes of the function (x²-16)/(x-4)

(4,8)

400

Holes of the function (x-4)/(x-4)

(4,1)

500

Holes of the function f(x)=(3x⁴+6x³+3x²)/(x²+2x+1)

(-1,3)

Vertical Asymptotes

100

The VA of the function x³/(x²-9)

x=3,-3

200

The VA of the function 2(x+3)(x-3)/(x+1)(x+5)

x=-1 x=-5

300

The VA of the function (x²-x-2)/(x-2)

none

400

The VA of the function (x³+x²-6x)/(4x²+4x-8)

x=-2,1

500

The VA of the function (x+3)/(x²+8x+15)

​​​​

x=-5

Horizontal Asymptotes

100

The HA of the function f(x)=x-2/x-4

y=1

200

The HA of the function x³/(x²-9)

y=none

300

The HA to the function 2(x+3)(x-3)/(x+1)(x+5)

y=2

400

The HA to the function 1/(3x²+3x-18)

y=none

500

The HA of the function (x²-4)/x²(x-3)

y=0