Answer
See graph.
Work Step by Step
Step 1. Given $f(x)=\frac{4x^2-9}{2x+3}=\frac{(2x+3)(2x-3)}{2x+3}=2x-3, (x\ne-3/2)$, we can identify its V.A. $none$, H.A. $none$, hole: $(-3/2, -6)$, x-intercepts: $x=3/2$, y-intercepts: $f(0)=-3$.
Step 2. Use the above information and test points to graph the function as shown in the figure.