Today in Pre-Calculus

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Today in Pre-Calculus

• Go over homework.
• Notes Asymptotes and End Behavior
• Need a calculator
• Homework

2

1. Unbounded
2. Bounded below b0
3. Bounded below b 1
4. Unbounded, (-8,0) bounded above B5, (0,8)
   bounded below b5
5. Bounded above B0
6. Bounded, b-1, B1
7. Bounded below b0
8. Bounded below b-1.006
9. Bounded below b0
10. Bounded above B0

3
Asymptotes

• Asymptotes vertical or horizontal lines the
  graph of a function does not cross
• This graph has
• two vertical asymptotes at x-1 and x2
• one horizontal asymptote at y0 as x
  approaches -8,8

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End Behavior

• Used to describe the behavior of a graph as x
  approaches 8 and -8.
• Describes what is happening to y-values at the
  left and right ends of the graph.
• Limit notation is used to describe end behavior
• In the example

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Example 1

• End behavior
• Asymptotes
• Horizontal y1
• Vertical x2

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Example 2

• End behavior
• Asymptotes Vertical x2, x-2

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Example 3

• End behavior
• Asymptotes Horizontal y2

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Example 4

• End behavior
• Asymptotes Horizontal y-2
• Vertical
• x1.731
• x-1.731

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Example 5

• End behavior
• Asymptotes
• Horizontal y2, y-4
• Vertical x0

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Homework

• Wkst.