Question

Identify the discontinuities, graph, and find the zeros of each rational function. f(x)=2x^2+5x-12/x+4

Answer 1

Notice that
\[
\frac{2 x^2+5 x-12}{x+4}=\frac{(2
x-3) (x+4)}{x+4}=2 x-3
\]
What can you conclude?

Answer 2

It has a removable singularity at x=-4

Answer 3

It has a zero at x =3/2

Answer 4

The graph is the line y= 2 x-3