Asymptotes

First you need to find the domain of the function. You do this by looking at the denominator of the function and then factoring it out. You will then look for real zeros. Non real zeros do not affect the domain since they are not on the real number line

After you find the domain of the function you should find the x value of the problem. you find the x value by factoring out the numerator and then you will find your x values by comparing them, or zeroing them.

I.E. (x-5)(x+1) To zero these you would set one of the x's= to (5-5=0) (-1+1=0)



find your y value by setting x to zero.

Then you need to find your Vertical Asymptote. You find this by using the the theorem of vertical asymptotes which states

If the real number @ is a zero of the denominator then the graph of the function
p/q where p and q have no common factors has the vertical asymptote of

x=@

Then find the Horizontal Asymptotes by using this theorem

a function with unlimited degree on numerator and denominator both degrading to a 0 degree(a real number usually) ie

be a rational function with the numerator of degree m and denominator of degree n

1.if the degree of of the numerator is less than the degree of the denominator then the x axis is the horizontal asymptote of graph F

2. If numerator is equal to the denominator then the line given by divide the numerator coefficient by the denominators coefficient

3. if the numerator is greater than the denominator there is no horizontal asymptote but

there is the possibility of having a slant asymptote if degree numerator is = degree denominator +1

remember they cannot have any common factors for a slant asymptote