Final answer:
The domain of the function f(x) = |x - 6| is all real numbers. The range of the function is all non-negative real numbers since the absolute value ensures the output is never negative.
Step-by-step explanation:
The student asked about the domain and range of the function f(x) = |x - 6|. To determine the domain and range of this function, we need to understand the properties of absolute value functions. The domain of a function is the set of all possible inputs (x-values) for which the function is defined. For f(x) = |x - 6|, the function is defined for all real numbers because you can take the absolute value of any real number. Therefore, the domain is all real numbers, or -∞ < x < ∞.
The range of a function refers to the set of all possible outputs (y-values). Since the absolute value operation results in a non-negative value, the smallest value f(x) can take is 0 (which occurs when x = 6). Hence, the range of f(x) = |x - 6| is 0 ≤ f(x) < ∞, meaning that f(x) can take on any value greater than or equal to zero.