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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 +...
View Full Document

This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

Page1 / 9

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online