Horizontal Asymptotes and Infinite Limits (8.5.2)

Question 1

What are asymptotes?

Answer 1

• Asymptotes are lines that the graph of a function approaches. A horizontal asymptote to the graph of a function f is a line whose equation is y = a, where lim x->∞ f(x) = a, or lim x->-∞ f(x) = a.

Question 2

How do you identify horizontal asymptotes?

Answer 2

• Identify horizontal asymptotes by taking the limit of the function as x approaches positive or negative infinity.

Question 3

• Examine the highest-powered term in the numerator and the highest-powered term in the denominator when determining the limit of a rational function. The expression ∞/∞ is an indeterminate form.

Answer 3

• Examine the highest-powered term in the numerator and the highest-powered term in the denominator when determining the limit of a rational function. The expression ∞/∞ is an indeterminate form.