Question

What is the graph of the function f(x) = -x^2-9x-20/x+4?

Answer 1

\[f(x) = \frac{ -x^2 - 9x - 20 }{ x+4}\]

Answer 2

My choices

Answer 3

First note that the function is undefined at x=-4 because you divide by 0. Then factor the top and see that one of the factors is conveniently (x+4) so you can cancel those out.\[f(x)=\frac{-x^2-9x-20}{x+4}=\frac{(x+4)(-x-5)}{x+4}=-x-5\]Now we have a simple equation of a line, but remember that it's undefined at x=-4 so you draw a hole there. The answer is the last one because it has a slope of -1, a y-intercept of -5, and a hole at x=-4.