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Show all work to identify the asymptotes and zero of the function f of x equals 3 x over quantity x squared minus 9.

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mhanifa

Answer:

  • Asymptotes: x = -3, x = 3, y = 0

Step-by-step explanation:

Given function:

  • f(x) = 3x / (x² - 9)

Zero of the function:

  • f(x) = 0
  • 3x / (x² - 9) = 0
  • x = 0, x ≠ -3; 3

Vertical asymptotes:

  • x² - 9 = 0
  • x² = 9
  • x = √9
  • x = -3; x = 3

Horizontal asymptotes:

  • The horizontal asymptote is y = 0, since the degree of the numerator is 1, while the degree of the denominator is 2.

The graph with asymptotes and zero is attached

Ver imagen mhanifa

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