Determine the domain and range of the following rational function: f(x) = ((x - 3)(x + 9)) / ((x + 1)(x -...

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1. Determine the domain and range of the following rational function: f(x) = ((x - 3)(x + 9)) / ((x + 1)(x - 3))
a. Domain: (-∞, 3) ∪ (3, ∞) Range: (∞, 0) ∪ (1, ∞)
b. Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞) Range: (-∞, ∞)
c. Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞) Range: (-∞, 0) ∪ (1, ∞)
d. Domain: (-∞, -1) ∪ (1, ∞) Range: (∞, 0) ∪ (1, ∞)
2. Determine the domain and range of the following rational function: f(x) = ((x + 7)(x - 3)) / ((x + 5)(x - 9)(x - 3))
a. (-∞, -5) ∪ (-5, 9) ∪ (9, ∞)
b. (-∞, -3) ∪ (-3, 5) ∪ (5, 9) ∪ (9, ∞)
c. (-∞, -5) ∪ (-5, 3) ∪ (3, 9) ∪ (9, ∞)
d. (-∞, 3) ∪ (3, 9) ∪ (9, ∞)

SnapAndSolve AI · Accepted Answer

The function f(x) = ((x - 3)(x + 9)) / ((x + 1)(x - 3)) has a removable discontinuity at x = 3 and a vertical asymptote at x = -1. The domain excludes x = -1 and x = 3. The range is all real numbers except for the horizontal asymptote at y = 1. Therefore, the correct answer is:

c. Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞) Range: (-∞, 0) ∪ (1, ∞)
The function f(x) = ((x + 7)(x - 3)) / ((x + 5)(x - 9)(x - 3)) has vertical asymptotes at x = -5, x = 9, and a removable discontinuity at x = 3. The domain excludes x = -5, x = 9, and x = 3. Therefore, the correct answer is:

c. (-∞, -5) ∪ (-5, 3) ∪ (3, 9) ∪ (9, ∞)

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Determine the domain and range of the following rational function: f(x) = ((x - 3)(x + 9)) / ((x + 1)(x -...

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