Question 983457
I will graph 3/(x^2-4)

The domain is all x's except x=2 and x=-2.  That makes the denominator 0.
y can be any positive number, for as x approaches 2 from either side, the value of the function approaches positive or negative infinity.  Y can be any negative number less than or equal to (-3/4).  This can be done from the graph or from taking the first derivative of the function, which shows a local maximum for x=0.
Horizontal asymptote is at y=0 for x less than -2 or x greater than 2.
Vertical asymptotes are at x=+/-2


{{{graph(300,200,-10,10,-10,10,3/(x^2-4))}}}