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Understanding Asymptotes: Domain, Range, and Vertical/Horizontal Characteristics

This guide provides an overview of asymptotes in mathematical functions, explaining their significance. Asymptotes are lines that graphs approach but do not intersect. We delve into vertical and horizontal asymptotes, defining them as values that function variables can never equal. For vertical asymptotes, we illustrate how to identify values of "x" that lead to undefined behavior, while horizontal asymptotes relate to "y" values the function approaches. Example functions illustrate these concepts for better understanding of domains and ranges.

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Understanding Asymptotes: Domain, Range, and Vertical/Horizontal Characteristics

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  1. Family Functions:Asymptotes

  2. What is the Domain and Range of this function?

  3. Asymptote A line that a graph gets closer and closer to, but never touches. -Vertical Asymptote: A value that our “x” can never be equal to. -Horizontal Asymptote: A value that our “y” can never be equal to.

  4. Vertical: 1 Horizontal: 0

  5. What is the vertical asymptote? x + 3 y = x - 2 x = 2

  6. What is the vertical asymptote? x² + 4x + 5 y = (x + 3)(x – 4) x = -3, 4

  7. What is the vertical asymptote? x² + 4x + 5 y = x² - 9 x = -3, 3

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