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Exploring Limits and Continuity in Functions: Horizontal Asymptotes, Values, and Continuity Analysis

Learn how to identify horizontal asymptotes, find values for continuity, and analyze continuity types in functions with clear examples and explanations.

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Exploring Limits and Continuity in Functions: Horizontal Asymptotes, Values, and Continuity Analysis

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  1. MATH(O) Limits and Continuity

  2. 1

  3. Identify the horizontal asymptote(s) for: • f(x) =-5 • f(x) = 4 • f(x) = -1 • f(x) = 0 • no horizontal asymptotes D

  4. Does Not Exist

  5. Based on the graph below, find:

  6. Identify the horizontal asymptote(s) for: • f(x) = -2 • f(x) = -1 • f(x) = 1/8 • f(x) = 3 • No horizontal asymptotes A

  7. Find the value of a so that f(x) is continuous for all values of x. 1/6

  8. Describe continuity of: • Continuous • Discontinuous non-removable at x = -6 • Discontinuous removable at x = -6 • Discontinuous non-removable at x = 0 C

  9. Describe continuity of: • Continuous • Discontinuous removable at x = -4 • Discontinuous removable at x = 4 • Discontinuous non-removable at x = 4 • Both B and C • Both B and D B

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