Question

Which graph represents the function?

Answer 1

The bottom factors to (x - 30(x + 2) so there are asymptotes at x = -2 and x = 3. Also y intercept id at (0,1) so its either graph 2 or graph 4.
Between x = 0 and x = 3 y is increasing so the correct graph is Graph 2.

Answer 2

Of course, I would just graph it on Desmos.com or my graphing calculator and be done.

f(x) can be factored as
.. f(x) = (x -6)(x +1)/((x -3)(x +2))

so will have zeros at x = {-1, 6}, vertical asymptotes at x = {-2, 3}, and sign changes at all of those points.

The Upper Right graph is the only one with the zeros and asymptotes in the right places.