SOLUTION: How do I find the end behavior function for the polynomial (2x^2-3x+5)/(x-2)? Thank you very much!

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Question 790962: How do I find the end behavior function for the polynomial (2x^2-3x+5)/(x-2)?
Thank you very much!
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Perform the division. You will find a quotient and a remainder. The denominator to use with the remainder will be (x-2). The quotient for this rational expression is 2x%2B1%2B7%2F%28x-2%29.

What happens to this expression as x tends to negative infinity without bound? What happens to this expression as x tends to positive infinity without bound? In both cases, the 7/(x-2) becomes increasingly small, and either positive or negative, but its absolute value becomes increasingly small. The other part, 2x+1 persists and is a slant asymptote, a line which the function approaches but never reaches.

graph%28400%2C400%2C-20%2C20%2C-20%2C20%2C%282x%5E2-3x%2B5%29%2F%28x-2%29%29

And actually to show the asymptote with the function,
graph%28400%2C400%2C-20%2C20%2C-20%2C20%2C%282x%5E2-3x%2B5%29%2F%28x-2%29%2C2x%2B1%29