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Determine the domain and range of the following rational function: f(x) = (4(x + 7)(x - 2)) / ((x - 3)(x +...

4. Determine the domain and range of the following rational function:
f(x) = (4(x + 7)(x - 2)) / ((x - 3)(x + 9))
A. Domain: (-∞, -9) ∪ (-9, 3) ∪ (3, ∞)
Range: (-∞, ∞)
B. Domain: (-∞, -9) ∪ (-9, ∞)
Range: (-∞, 4) ∪ (4, ∞)
C. Domain: (-∞, -9) ∪ (3, ∞)
Range: (-∞, 4) ∪ (4, ∞)
D. Domain: (-∞, -9) ∪ (-9, 3) ∪ (3, ∞)
Range: (-∞, ∞) ∪ (4, ∞)

Answer

Correct Answer: C

  1. Domain: The function is undefined where the denominator is zero. The denominator is (x - 3)(x + 9), so x cannot be 3 or -9. Thus, the domain is (-∞, -9) ∪ (3, ∞).
  2. Range: The range is all real numbers except where the function has horizontal asymptotes. The horizontal asymptote is y = 4, so the range is (-∞, 4) ∪ (4, ∞).

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