Question 1002513
Written correctly, you are  asking for f(x)=(x^2+x-30)/(x-7).
<pre>


Synthetic Division as if checking root of 7


7     |    1      1     -30 
      |           7     56
      |_____________________________________
          1       8     26     
</pre>
The quotient line means  {{{x+8+26/(x-7)}}}.  The rational part approaches 0 as x goes unbounded, so the slant asymtptote is {{{highlight(y=x+8)}}}.



Try to factorize the function.
{{{((x-5)(x+6))/(x-7)}}}


Let x=0 to find y axis intercept.
{{{y=(0-5)(0+6)/(0-7)}}}
{{{highlight(y=30/7)}}}-------y-intercept.


Look at the numerator factors for the x-intercepts.
They are  (5,0) and (-6,0).


Vertical asymptote is where f is undefined:
{{{highlight(x=7)}}}-----vertical asymptote



{{{graph(300,300,-10,35,-10,35,(x^2+x-30)/(x-7))}}}