Alg2 lesson 9-3
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This document discusses key concepts for graphing rational functions: 1) Vertical and horizontal asymptotes are determined by factors in the denominator that do or do not cancel out. A vertical asymptote is indicated at x = -3 and there is a hole at x = -2. 2) The horizontal asymptote is the line y = 1. 3) Examples are provided to demonstrate graphing rational functions based on identifying discontinuities and asymptotes.
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Alg2 lesson 9-3
- 1. Vertical Asymptotex = 4HoleHorizontal AsymptoteAt x = -2y = 1
- 2. Graphing rational functionsFactor numerator and denominatorDiscontinuities occur where denominator equals zeroHoles are indicated by factors of denominator that cancel out
- 3. Vertical asymptotes are indicated by factors of denominator that do not cancelHorizontal Asymptotes (predict end behavior) – look at highest degree term of numerator and denominatorDegree of top > degree of bottom: no HA
- 4. Degree of top < degree of bottom: HA is y = 0
- 5. Degrees equal: HA is y = Determine the equations of any asymptotes and the values of x for any holes in the graph of Undefined for x = –2 and –3Hole at x = -2Vertical asymptote is the line x = -3Horizontal asymptote: the line y = 1 Example 3-1a
- 6. GraphVA: x = -3HA: y = 1Hole at x = -2(-2, -4)-2= -4-2
- 7. Graphx-8/-3 or 8/3-7/-2 or 7/2-6/-1 or 6-3/2-2/3-1/4-6-5-4-101
- 8. GraphVA: x = –1No holesHA: y = 1Example 3-2a
- 10. GraphUndefined for x = 2(2, 4)Hole at x = 22x-101123Example 3-3a