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L17 - Lecture 17 Section 2.6 Rational Functions Holes and...

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Unformatted text preview: Lecture 17: Section 2.6 Rational Functions Holes and Vertical Asymptotes The graph of a rational function u1D453 ( u1D465 ) = u1D45D ( u1D465 ) u1D45E ( u1D465 ) has a hole at u1D465 = u1D44E if 1. both u1D45D ( u1D465 ) and u1D45E ( u1D465 ) have the common factor ( u1D465 − u1D44E ), and 2. the simplified denominator DOES NOT have the factor ( u1D465 − u1D44E ). NOTE: To find the u1D466-coordinate of the hole in the graph, plug u1D465 = u1D44E into the simplified expression of u1D453 ( u1D465 ). ex. Find all vertical asymptotes and holes of the function: 1) u1D453 ( u1D465 ) = u1D465 + 1 u1D465 2 − u1D465 − 2 2) u1D454 ( u1D465 ) = 2 u1D465 3 ( u1D465 + 1)( u1D465 − 3) u1D465 ( u1D465 + 1) 2 ( u1D465 − 2)( u1D465 − 3) Horizontal Asymptotes Def. The line u1D466 = u1D43F is a horizontal asymptote (HA) of the graph u1D466 = u1D453 ( u1D465 ) if To Find Horizontal Asymptotes: Let u1D453 ( u1D465 ) = u1D45D ( u1D465 ) u1D45E ( u1D465 ) = u1D44E u1D45B u1D465 u1D45B + ⋅⋅⋅...
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L17 - Lecture 17 Section 2.6 Rational Functions Holes and...

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