Question

How do you graph `f(x)=(x+4)/(-2x-6)` using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer 1

You may rewrite to `f(x)=-1/2 xx(x+4)/(x+3)`

Explanation:

The vertical asymptote will then be clear: `x=-3` as the demoninator may not be `=0`

If `x` gets larger and larger (both netaive or positive), the `+4` and `-3` matter less and the function will converge to:
`-1/2 xx x/x=-1/2`

So `y=-1/2` is the horizontal asymptote .
graph{(x+4)/(-2x-6) [-11.25, 11.25, -5.625, 5.625]}