SOLUTION: How to determine where rational functions will come from? for example: (8x-4x^2)/(x+2)^2 I found the x-y intercepts and horizontal/vertical asymptotes. I know it can't pa

Algebra ->  Rational-functions -> SOLUTION: How to determine where rational functions will come from? for example: (8x-4x^2)/(x+2)^2 I found the x-y intercepts and horizontal/vertical asymptotes. I know it can't pa      Log On


   

Question 951126: How to determine where rational functions will come from?
for example:
(8x-4x^2)/(x+2)^2
I found the x-y intercepts and horizontal/vertical asymptotes. I know it can't pass through the vertical but it can pass through the horizontal. My question is how do I know where the line will come from. I graphed it online and it showed the line entering from the right side above the horizontal line through the -2 up and down through the origin and back down idling the vertical asymptote. But how can I determine how the line will behave?

Thank you
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
"where will the/a graph come from?" The question does not mean what you discussed.

Look at factorization.

4%282-x%5E2%29%2F%28x%2B2%29%5E2

-4%28x%5E2-2%29%2F%28x%2B2%29%5E2

Two irrational zeros, meaning crosses the x axis in two places.
x%5E2=2
x=-sqrt%282%29 and at x=sqrt%282%29.

Vertical asymptote at x=-2. The function is undefined at x=-2.

For unbounded x left or right, the function will approach -4x%5E2%2Fx%5E2 or -4, which means the line y=-4 is the horizontal asymptote.


?
Something is not right about this analysis or the graphs.....
graph%28300%2C300%2C-12%2C12%2C-12%2C12%2C%288x-4x%5E2%29%2F%28x%2B2%29%5E2%29

graph%28300%2C300%2C-12%2C12%2C-22%2C2%2C%288x-4x%5E2%29%2F%28x%2B2%29%5E2%29

graph%28300%2C300%2C-32%2C32%2C-22%2C22%2C%288x-4x%5E2%29%2F%28x%2B2%29%5E2%29

graph%28300%2C300%2C-4%2C4%2C-4%2C4%2C%288x-4x%5E2%29%2F%28x%2B2%29%5E2%29