SOLUTION: f(x)=x^2-36/x+6 I need help graphing this rational function. Thank you so much for your help!!

Algebra ->  Rational-functions -> SOLUTION: f(x)=x^2-36/x+6 I need help graphing this rational function. Thank you so much for your help!!      Log On


   

Question 142513: f(x)=x^2-36/x+6
I need help graphing this rational function.
Thank you so much for your help!!
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
I knew this one was coming, or one like it!! In this case, you cannot divide by zero, so x must NOT be allowed to equal -6. Now, having said that, if you reduce the fraction, you get:
f%28x%29+=+%28x%5E2-36%29%2F%28x%2B6%29+
f%28x%29+=+%28%28x-6%29%28x%2B6%29%29%2F%28x%2B6%29 which reduces to f%28x%29+=+%28x-6%29+, but x MUST NOT EQUAL -6!

The comment above that x cannot equal -6 is very important!! This essentially places a HOLE in the graph!! The graph is a straight line with a hole in it. If you use a graphing calculator, you will see a straight line, but the hole in the graph will not show up, unless you know to look for it. Even then, you probably won't be able to see it.

graph%28300%2C600%2C+-10%2C10%2C-20%2C20%2C+%28x%5E2-36%29%2F%28x%2B6%29+%29 but there is a HOLE in the graph at x=-6!

Probably your next question will be f%28x%29+=+%28x%2B6%29%2F%28x%5E2-36%29+. This graph has an asyptote at x=6 and a hole in the graph at x=-6.

R^2