Final answer:
The domain of the function f(x) = (x + 1)^2 - 7 is all real numbers, and the range is [-7, ∞).
Step-by-step explanation:
The domain of a function is the set of all possible inputs (x-values) for which the function is defined, and the range is the set of all possible outputs (y-values). For the function f(x) = (x + 1)^2 - 7, since there are no restrictions on the x-values in the equation (such as division by zero or taking the square root of a negative number), the domain is all real numbers (-∞, ∞). To find the range, we observe that the lowest value of (x + 1)^2 is 0 (when x = -1), which corresponds to f(x) being -7. Since (x + 1)^2 increases without bound as x moves away from -1, the range of f(x) is [-7, ∞).