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Identify the vertical asymptotes of the following rational function: f(x) = (x - 5) / ((x + 2)(x - 7)) a. x...

15. Identify the vertical asymptotes of the following rational function:
f(x) = (x - 5) / ((x + 2)(x - 7))
a. x = 5
b. x = 2, -7
c. x = -5
d. x = -2, 7

Answer

The vertical asymptotes of a rational function occur where the denominator is equal to zero, provided the numerator is not zero at those points. For the function f(x) = (x - 5) / ((x + 2)(x - 7)), set the denominator equal to zero:

  1. (x + 2)(x - 7) = 0
  2. x + 2 = 0 or x - 7 = 0
  3. x = -2 or x = 7

Therefore, the vertical asymptotes are at x = -2 and x = 7. The correct answer is d. x = -2, 7.

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