Explain how to use end behaviour to find the equation of the horizontal asymptote of a rational function.

Answer 1

just ignore everything but the highest power in the numerator and denominator

So, (3x^3-5x+2)/(2x^3+9x^2-100) looks like
3x^3/2x^2 = 3/2
for large x.

Or, you can think of it like this. Divide top and bottom by the highest power. That gives you

(3-5/x^2+2/x^3)/(2+9/x-100/x^3)

For large x, the fractions all go to zero, and we are just left with 3/2.

So, as x goes way out on the axis, y just approaches 3/2, the horizontal asymptote.