Question

State the domain of the rational function: y = x-2/x+4 Responses A (-∞, ∞)(-∞, ∞) B (-∞, -4) ∪ (-4, ∞)(-∞, -4) ∪ (-4, ∞) C (-∞, 0) ∪ (0, ∞)(-∞, 0) ∪ (0, ∞) D (-∞, 1) ∪ (1, ∞)(-∞, 1) ∪ (1, ∞) E (-∞, 2) ∪ (2, ∞)(-∞, 2) ∪ (2, ∞)

Answer 1

The domain of the rational function y = (x-2)/(x+4) is all real numbers except x = -4, so the correct choice is option B (-∞, -4) ∪ (-4, ∞).

Step-by-step explanation:

We need to find the domain of the rational function y = \( \frac{x-2}{x+4} \). The domain of a function is the set of all possible inputs (x-values) for which the function is defined. The only restriction for a rational function is that the denominator cannot be zero because division by zero is undefined.

Looking at the function y = \( \frac{x-2}{x+4} \), we can see that the denominator becomes zero when x = -4. Therefore, x = -4 is not in the domain of the function. The domain is all real numbers except x = -4.

The correct choice is option B (-∞, -4) ∪ (-4, ∞), which represents all real numbers except -4.