Vertical and Horizontal Asymptotes: To find the vertical asymptote, set the denominator equal to zero. To find the horizontal asymptote, look at the exponents. There are three possible ways to solve for the horizontal: if the exponent is larger in the numerator, there is no asymptote. If the exponent is larger in the denominator, then y=0. If they are equal, take the number in front of the exponent.
Example: x^2 + x -20/x^2 +7x + 10 Vertical: -2
Description: Factor everything possible. Horizontal: 1.
On the top you get (x-4)(x+5) Hole: (-5,-3)
On the bottom: (x+2)(x+5) Domain: (xlx cannot = -2,-5, x E of the reals)
The easiest way to start the process is to find the holes.
The x+5 cancels so set that equal to zero. You get -5
then you plug that back into whatever is left on the bottom.
You get (-5 +2) when you plug it in. So your Hole is (-5,-3).
To find the domain set the remaining equal to zero in the denominator.
Set x+2=0 and you get -2. To find the Horizontal, look at the exponents.
They match so take the coefficient (1/1) so you get 1. For the domain use the denominator
and write in set-builder notation.
Example: x^2 + x -20/x^2 +7x + 10 Vertical: -2
Description: Factor everything possible. Horizontal: 1.
On the top you get (x-4)(x+5) Hole: (-5,-3)
On the bottom: (x+2)(x+5) Domain: (xlx cannot = -2,-5, x E of the reals)
The easiest way to start the process is to find the holes.
The x+5 cancels so set that equal to zero. You get -5
then you plug that back into whatever is left on the bottom.
You get (-5 +2) when you plug it in. So your Hole is (-5,-3).
To find the domain set the remaining equal to zero in the denominator.
Set x+2=0 and you get -2. To find the Horizontal, look at the exponents.
They match so take the coefficient (1/1) so you get 1. For the domain use the denominator
and write in set-builder notation.