SOLUTION: State the horizontal asymptote of the rational functions. (these were separate questions but I had to do the same thing on both.) f(x) = (7x^2 - 3x -9)/(2x^2 - 4x+5) f(x) =

Algebra ->  Test -> SOLUTION: State the horizontal asymptote of the rational functions. (these were separate questions but I had to do the same thing on both.) f(x) = (7x^2 - 3x -9)/(2x^2 - 4x+5) f(x) =       Log On


   

Question 1061131: State the horizontal asymptote of the rational functions.
(these were separate questions but I had to do the same thing on both.)
f(x) = (7x^2 - 3x -9)/(2x^2 - 4x+5)

f(x) = (x+9)/(x^2+ 2x+5)


Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
Your second function and the question seem more interesting.

%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29 has a sign change at x=-9. Denominator is not factorable, and denominator is positive for all x values.

Think how the rational expression goes as x tends either toward negative infinity or toward positive infinity. The denominator increases in size MORE THAN the numerator. This function will become increasingly closer to 0 to the left, and become increasingly closer to zero to the right. Horizontal asymptote is y=0.

graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29%29

Same thing closer look:
graph%28300%2C300%2C-9%2C9%2C-3%2C3%2C%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29%29