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

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) (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.

Two irrational zeros, meaning crosses the x axis in two places.

and at .

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

For unbounded x left or right, the function will approach or -4, which means the line is the horizontal asymptote.

?
Something is not right about this analysis or the graphs.....

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