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Functions, Graphs, and Limits

Functions, Graphs, and Limits

Slant Asymptotes

A slant asymptote, also known as an oblique asymptote, is an asymptote that's a straight (but not horizontal or vertical) line of the usual form y = mx + b (in other words, a degree-1 polynomial). A function with a slant asymptote might look something like these:

If a function f(x) has a slant asymptote as x approaches ∞, then the limit does not exist, because the function must grow without bound to stay close to the slant asymptote.

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