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College Algebra / Unit 7   Alg 381 short lesson, about 20 seconds

Horizontal Asymptotes

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The idea

A horizontal asymptote is the line outputs approach for far inputs, set by degrees: bottom-heavy gives y = 0, equal gives the leading-coefficient ratio, top-heavy gives none.

In practice

(x² − 9)/(x² + 5x + 6) has equal degrees, so y = 1 — at 1000 the output is 0.995, hugging the line.

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