Using limits to detect asymptotes

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After completing this section, students should be able to do the following.

Recognize when a limit is indicating there is a vertical asymptote.
Evaluate the limit as $x$ approaches a point where there is a vertical asymptote.
Match graphs of functions with their equations based on vertical asymptotes.
Discuss what it means for a limit to equal $\infty$ .
Define a vertical asymptote.
Find horizontal asymptotes using limits.
Produce a function with given asymptotic behavior.
Recognize that a curve can cross a horizontal asymptote.
Understand the relationship between limits and vertical asymptotes.
Calculate the limit as $x$ approaches $\pm \infty$ of common functions algebraically.
Find the limit as $x$ approaches $\pm \infty$ from a graph.
Define a horizontal asymptote.
Identify horizontal asymptotes by looking at a graph.
Identify vertical asymptotes by looking at a graph.