𝑦 = (3x^2)/(x^2-4)

Question

Determine equation of vertical asymptotes. For vertical asymptotes, investigate function values
on either side of the asymptote

I know that the vertical asymptotes is located at x = -2, 2, but I don't understand what the questions means by "For vertical asymptotes, investigate function values on either side of the asymptote." How do we find/solve for it?

Answer 1

consider the asymptote at x=2
at x=2.01, y>0
at x = 1.99, y<0
so the graph plunges down from +∞ on the right, and plunges down to -∞ on the left of the asymptote at x=2

the reverse happens near x = -2
so the graph looks like an inverted parabola between the asymptotes, and mirror hyperbolas (as in y=1/x) outside the asymptotes.

consult any handy online graphing site to see this.