SOLUTION: Determine the equation of the horizontal asymptote of the function. If the function does not have a horizontal asymptote, explain why. You must write the answer in an equation.

Algebra ->  Equations -> SOLUTION: Determine the equation of the horizontal asymptote of the function. If the function does not have a horizontal asymptote, explain why. You must write the answer in an equation.       Log On


   

Question 1068030: Determine the equation of the horizontal asymptote of the function. If the function does not have a horizontal asymptote, explain why. You must write the answer in an equation.
f(x) = (2x-3x^2)/(2x^2-x-3)
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%282x-3x%5E2%29%2F%282x%5E2-x-3%29

f%28x%29=%282x-3x%5E2%29%2F%282x%5E2-x-3%29+=%28-3x%5E2%2B2x%29%2F%282x%5E2-x-3%29

The leading terms of numerator and denominator are of equal degree, and these leading terms become increasingly important for extreme x values to the left or to the right. The ratio of their coefficients become the horizontal asymptote. 
highlight%28y=-3%2F2%29      Horizontal Asymptote