Alg2 lesson 9-3

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Alg2 lesson 9-3

  1. 1. Vertical Asymptote<br />x = 4<br />Hole<br />Horizontal Asymptote<br />At x = -2<br />y = 1<br />
  2. 2. Graphing rational functions<br />Factor numerator and denominator<br />Discontinuities occur where denominator equals zero<br /><ul><li>Holes are indicated by factors of denominator that cancel out
  3. 3. Vertical asymptotes are indicated by factors of denominator that do not cancel</li></li></ul><li>Horizontal Asymptotes (predict end behavior) – look at highest degree term of numerator and denominator<br /><ul><li>Degree of top > degree of bottom: no HA
  4. 4. Degree of top < degree of bottom: HA is y = 0
  5. 5. Degrees equal: HA is y = </li></li></ul><li>Determine the equations of any asymptotes and the values of x for any holes in the graph of <br />Undefined for x = –2 and –3<br />Hole at x = -2<br />Vertical asymptote is the line x = -3<br />Horizontal asymptote:<br /> the line y = 1 <br />Example 3-1a<br />
  6. 6. Graph<br />VA: x = -3<br />HA: y = 1<br />Hole at x = -2<br />(-2, -4)<br />-2<br />= -4<br />-2<br />
  7. 7. Graph<br />x<br />-8/-3 or 8/3<br />-7/-2 or 7/2<br />-6/-1 or 6<br />-3/2<br />-2/3<br />-1/4<br />-6<br />-5<br />-4<br />-1<br />0<br />1<br />
  8. 8. Graph<br />VA: x = –1<br />No holes<br />HA: y = 1<br />Example 3-2a<br />
  9. 9. Graph<br />Example 3-2b<br />
  10. 10. Graph<br />Undefined for x = 2<br />(2, 4)<br />Hole at x = 2<br />2<br />x<br />-1<br />0<br />1<br />1<br />2<br />3<br />Example 3-3a<br />

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