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# Alg2 lesson 9-3

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### Alg2 lesson 9-3

1. 1. Vertical Asymptote x=4Hole Horizontal AsymptoteAt x = -2 y=1
2. 2. Graphing rational functions1. Factor numerator and denominator2. Discontinuities occur where denominator equals zero • Holes are indicated by factors of denominator that cancel out • Vertical asymptotes are indicated by factors of denominator that do not cancel
3. 3. 3. Horizontal Asymptotes (predict end behavior) – look at highest degree term of numerator and denominator • Degree of top > degree of bottom: no HA • Degree of top < degree of bottom: HA is y = 0 • Degrees equal: HA is y =
4. 4. Determine the equations of any asymptotes and thevalues of x for any holes in the graph of Undefined for x = –2 and –3 Hole at x = -2 Vertical asymptote is the line x = -3 Horizontal asymptote: the line y = 1
5. 5. GraphVA: x = -3HA: y = 1Hole at x = -2 (-2, -4) -2 = -4 -2
6. 6. Graphx-6 -8/-3 or 8/3-5 -7/-2 or 7/2-4 -6/-1 or 6-1 -3/20 -2/31 -1/4
7. 7. GraphVA: x = –1No holesHA: y = 1
8. 8. Graph x f (x) –4 -4/-3 = 4/3 –3 -3/-2 = 3/2 –2 -2/-1 = 2 0 0/1 = 0 1 1/2 2 2/3 3 3/4
9. 9. Graph Undefined for x = 2Hole at x = 2 (2, 4) 2 x -1 1 0 2 1 3