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

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Answer 1 · 2017-07-10T11:32:51

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

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]}

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