Question

State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal asymptote. (5 points)
f(x)= x^2+3x-2/x-2

Answer 1

So here are the rules of horizontal asymptotes:

• Degree of Numerator > Degree of Denominator: No horizontal asymptote
• Degree of Numerator = Degree of Denominator: $y=\frac{\textsf{leading coefficient of numerator}}{\textsf{leading coefficient of denominator}}$
• Degree of Numerator < Degree of Denominator: y = 0

Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that this function has no horizontal asymptote.