Question

For the function f(x) = –(x 1)² + 4, identify the vertex, domain, and range.

a. The vertex is (–1, 4), the domain is all real numbers, and the range is y ≥ 4.
b. The vertex is (–1, 4), the domain is all real numbers, and the range is y ≤ 4.
c. The vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4.
d. The vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.

Answer 1

The vertex of the function f(x) = –(x 1)² + 4 is (-1, 4). The domain is all real numbers and the range is y ≤ 4.

Step-by-step explanation:

The vertex of the function f(x) = –(x 1)² + 4 is (-1, 4). The domain of the function is all real numbers, since there are no restrictions on the input. The range of the function is y ≤ 4, because the highest possible value for y is 4 and the function is decreasing as x increases.

To find the vertex, we can use the formula x = -b/2a, where a is the coefficient of x², b is the coefficient of x, and c is the constant term. In this case, a is -1 and b is 0, so the vertex is at x = -0/(-2) = -1. Plugging this value into the function, we get y = –(-1 1)² + 4 = –(0)² + 4 = 4.