Question
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Let
This function has:
  1. Ay intercept at the point
  2. intercepts at the point(s)
  3. Vertical asymptotes at
  4. Horizontal asymptote at

Ask by Whittaker Daniel. in the United States
Nov 22,2024

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Answer

  1. y-intercept at
  2. x-intercepts at and
  3. Vertical asymptotes at and
  4. Horizontal asymptote at

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Beyond the Answer

To find the intercepts, asymptotes, and characteristics of the function :
  1. The -intercept occurs when :
    So, the -intercept is at the point .
  2. The -intercepts occur when the numerator equals zero . Factoring gives:
    Thus, the -intercepts are at the points and .
  3. For vertical asymptotes, set the denominator equal to zero:
    Using the quadratic formula:
    This gives and . So, the vertical asymptotes are at and .
  4. For the horizontal asymptote, compare the leading coefficients of the numerator and denominator:
    Therefore, the horizontal asymptote is at .
In summary:
  1. -intercept at
  2. -intercepts at and
  3. Vertical asymptotes at and
  4. Horizontal asymptote at

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