Final answer:
Yes, if the domain of a piecewise-defined function f is all real numbers, then the range of f must also be all real numbers.
Step-by-step explanation:
Yes, if the domain of a piecewise-defined function f is all real numbers, then the range of f must also be all real numbers.
A piecewise-defined function is a function that is defined by different rules on different parts of its domain.
In this case, we are told that f is a horizontal line for 0 ≤ x ≤ 20, which means that the value of f is constant within that interval.
Since the domain of f is all real numbers, there are no restrictions on the possible values of x.
Therefore, the range of f will also be all real numbers, as the value of f can be any real number.