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Determine the asymptotes of the following rational function: f(x) = (x + 3) / (x - 2) a. Vertical: y = 1,...

1. Determine the asymptotes of the following rational function: f(x) = (x + 3) / (x - 2)
a. Vertical: y = 1, Horizontal: x = 2
b. Vertical: x = 1, Horizontal: y = 2
c. Vertical: x = 2, Horizontal: y = 1
d. Vertical: y = 2, Horizontal: x = 1
2. Determine the x-intercept of the following rational function: f(x) = (x - 3) / (x + 2)
a. (0, -3/2)
b. (0, 3)
c. (3, 0)
d. (-3/2, 0)

Answer

  1. The vertical asymptote is found by setting the denominator equal to zero: x - 2 = 0, so x = 2. The horizontal asymptote is determined by comparing the degrees of the numerator and denominator. Since they are the same, the horizontal asymptote is y = 1. Therefore, the correct answer is c. Vertical: x = 2, Horizontal: y = 1.

  2. The x-intercept is found by setting the numerator equal to zero: x - 3 = 0, so x = 3. Therefore, the x-intercept is (3, 0). The correct answer is c. (3, 0).

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