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 1067304: 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 KMST(5328) 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=%28-3x%5E2%2B2x%29%2F%282%28x%5E2-0.5x-1.5%29%29=%28-3x%5E2%2B1.5x%2B4.5%29%2F%282%28x%5E2-0.5x-1.5%29%29+%280.%0D%0A5x-4.5%29%2F%282%28x%5E2-0.5x-1.5%29%29=-3%2F2+%280.%0D%0A5x-4.5%29%2F%282%28x%5E2-0.5x-1.5%29%29
So, lim%28x-%3Einfinity%2Cf%28x%29%29=-3%2F2 .
The horizontal asymptote is highlight%28y=-3%2F2%29%0D%0A .
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C-3%2F2%2C%282x-3x%5E2%29%2F%282x%5E2-x-3%29%29