Question 6589
You shoud write it as 

{{{ f(x)= (x^2 - 10x + 24) /   (x + 9) }}} (click on view source to see how I did it)

Find the roots of the numerator:

*[invoke quadratic "x", 1, -10, 24]

They are in points 6, 4. Denominator has root x=-9. At that point -9, there is discontinuity similar to how 1/x behaves around 0.

When x approaches plus/minus infonity, this function approaches a straight line.

{{{ graph( 500, 400, -100, 100, -100, 100, (x^2 - 10x + 24) /   (x + 9) ) }}}

the graph is not great, there is a complete discontinuity around x=-9.