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Identify the vertical asymptotes and horizontal asymptote of each. 1) f(x) = (x^2 + 2x - 3) / (x^2 - x) 2)...

Identify the vertical asymptotes and horizontal asymptote of each.
1) f(x) = (x^2 + 2x - 3) / (x^2 - x)
2) f(x) = (3x - 3) / x

Answer

  1. Vertical Asymptotes: Set the denominator equal to zero: x^2 - x = 0. Factor to get x(x - 1) = 0, so x = 0 and x = 1 are vertical asymptotes.
    Horizontal Asymptote: Since the degrees of the numerator and denominator are equal, divide the leading coefficients: y = 1.

  2. Vertical Asymptotes: Set the denominator equal to zero: x = 0, so x = 0 is a vertical asymptote.
    Horizontal Asymptote: Since the degrees of the numerator and denominator are equal, divide the leading coefficients: y = 3.

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