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Lesson 27: How do we get a Hole in the graph?

Lesson 27: How do we get a Hole in the graph? . What is a hole in the Graph? . Vertical Asymptotes occur where the Example: Determine the domain of the below: So 5 is NOT a zero , is there a VA? Let’s use the Calc  Table to find the limit: Limit = 0.4, not plus or minus infinity

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Lesson 27: How do we get a Hole in the graph?

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  1. Lesson 27: How do we get a Hole in the graph?

  2. What is a hole in the Graph? • Vertical Asymptotes occur where the • Example: Determine the domain of the below: • So 5 is NOT a zero , is there a VA? • Let’s use the Calc  Table to find the limit: • Limit = 0.4, not plus or minus infinity • BUT f(5) is undefined • This is an OPEN POINT or Hole in the graph at (5,0.4)

  3. Example: Estimate VA’s and Holes in graph for the below function

  4. General Rule: VA’s and Holes in Graph • Shared (cancelled) factors in the denominator produce an open point (hole) • Uncancelled factors in the denominator produce VA’s • Draw the graph for the previous example using the table, VA’s and open point

  5. Example:

  6. CFU • To find the y-coord, you can also plug in the x-value into the remaining portion of the function

  7. If time, Let’s graph the HW Example

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