Answer
(a) See graph.
(b) $(-\infty,-6]U[1,2)U(2,\infty)$
Work Step by Step
(a) Factor the function to get $f(x)=\frac{(x+6)(x-1)}{(x-2)^2}$. We have V.A. $x=2$, H.A. $y=1$, x-intercepts $x=-6,1$, y-intercept $y=-\frac{3}{2}$. Use additional test values to plot. See graph.
(b) Use the graph, for $f(x)\ge0$, the solution intervals are $(-\infty,-6]U[1,2)U(2,\infty)$
