SOLUTION: I am having trouble figuring out if the following equation has point discontinuity, vertical asymptote, or both. {{{ f(x)= x^2 - 10x + 24 / x + 9 }}} (I couldn't figure out how

Question 6589: I am having trouble figuring out if the following equation has point discontinuity, vertical asymptote, or both.
(I couldn't figure out how to edit it to show this to you, but it is not 24/x, rather it is x^2 - 10x + 24 ALL over x + 9.)
Thanks
Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
You shoud write it as
(click on view source to see how I did it)
Find the roots of the numerator:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, 4. Here's your graph:

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.

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