Question 892246
<i>f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6</i>

One may guess that you have {{{f(x)=(9x^2+9x-18)/(3x+6)}}} which should be simplified.
{{{f(x)=(9/3)((x^2+x-2)/(x+2))}}}
{{{highlight(f(x)=3(((x+2)(x-1))/(x+2)))}}}


This will have a HOLE at x=-2, although seeing it on the graph on the site will be difficult
or impossible.  A zero occurs at x=1.  As x goes increasingly large or small (tend toward pos or neg
infinity), f approaches {{{y=3(x-1)=3x-3}}}.  Critical values of x are -2 and 1, so the signs in
the three intervals should be examined.


{{{graph(300,300,-6,6,-10,10,3((x^2+x-2)/(x+2)))}}}
Be aware again, a hole occurs at x=-2, f being undefined there.