**Beware!!! Many answers possible. **
•(5x^2)/(x^2 + 4)
This example will have a horizontal asymptote at y = 5 (since the ratio between the highest degrees = 5) and no vertical asymptote (since if x^2 + 4 = 0 -> x^2 = -4 -> x = O/).
You will have a horizontal asymptote at y = 5 anytime that the degree of the denominator equals that of the numerator and the ratio between the numerator and the denominator equals 5. If that is the only asymptote, the denominator when set to 0 like in the example above needs to have no solution; otherwise there will be vertical asymptotes.
Practice exercises:
1. Determine an equation for a rational function with a horizontal asymptote at y = -2
2. Determine an equation for a rational function with vertical asymptotes at x = -3 and x = 5 and a horizontal asymptote at y = 7.
Hopefully this helps, and good luck!
