Answer:
Domain: All real numbers
Range: f(x) ≥ - 11
Step-by-step explanation:
Given the quadratic function in vertex form, f(x) = ½(x + 4)² - 11:
The vertex, (h, k) is (-4, -11).
Range: f(x) ≥ -11.
The parabola opens upward (where a = ½, which is greater than 0), and k = -11 is the minimum value for f(x). Hence, the range of the given function must be at least -11, or f(x) ≥ -11.
Domain: all real numbers
There is no restriction for the value of x. Therefore, the domain of the given function is all real numbers.
