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Today in Pre-Calculus

Learn about asymptotes and end behavior in pre-calculus. Identify vertical and horizontal asymptotes. Understand end behavior as x approaches infinity. Homework and a quiz on September 22. Need a calculator.

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Today in Pre-Calculus

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  1. Today in Pre-Calculus • Go over homework. • Notes: Asymptotes and End Behavior • Need a calculator • Homework • Quiz: Tuesday, September 22

  2. Asymptotes • Asymptotes: vertical or horizontal lines the graph of a function does not cross • This graph has: two vertical asymptotes at x=-1 and x=2 one horizontal asymptote at y=0 as x approaches -∞,∞

  3. End Behavior • Used to describe the behavior of a graph as x approaches ∞ and -∞. • 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:

  4. Example 1 • End behavior: • Asymptotes: Horizontal: y=1 Vertical: x=2

  5. Example 2 • End behavior: • Asymptotes: Vertical: x=2, x=-2

  6. Example 3 • End behavior: • Asymptotes: Horizontal y=2

  7. Example 4 • End behavior: • Asymptotes: Horizontal y=-2 Vertical: x=1.731 x=-1.731

  8. Example 5 • End behavior: • Asymptotes: Horizontal y=2, y=-4 Vertical: x=0

  9. Homework • Wkst.

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