i am having trouble graphing functions i missed the lesson an i'm lost for example:

\(\displaystyle y=\frac{x}{x^2-4} \)

i know it has V.A at x=-2,x=2 and H.A. at y=0 because the degree of the denominator > degree of numerator

but where do i go from here?(figuring out odd and even asymptotes, x and y intercepts) etc....

You can get the first derivative to find out on which intervals it is decresing/increasing. You can use the info to know on which side of each vertical asymptote does the function go to (positive or negative infinity).

You can use the second derivative to get the concavity. that might help.

To get the x intercept(s), set y = 0 and solve for x.

To get the y intercept(s), set x = 0 and solve for y.

Don't forget that as the function goes to positive or negative infinity, it must converge to y = 0 (horizontal asymptote, as you've mentioned)..

Cheers!