There are times when we want to see how a function behaves near a horizontal asymptote. Much like finding the limit of a function as x approaches a value, we can find the limit of a function as x approaches positive or negative infinity. In this section, we will learn how to evaluate limits at infinity algebraically using the "Highest Power Rule", with tricks like using conjugates, common denominators, and factoring.
Express all asymptotes in limit notations for the function f whose graph is shown below.
Introduction to Horizontal Asymptotes
Use "Highest Power Rule" to Evaluate Limits at Infinity of Rational Functions in 3 Types
Multiply Conjugates First, then Evaluate Limits
Limits at infinity - horizontal asymptotes
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