Final answer:
The range of a piecewise function described as a horizontal line is the constant y-value that the line represents. Assuming f(x) is a horizontal line for x between 0 and 20, the range would be the constant value that f(x) equals regardless of x.
Step-by-step explanation:
The student has asked about finding the range of the given piecewise function f. Unfortunately, the exact definition of the function f(x) is not provided, however, the student seems to describe a horizontal line. A horizontal line on a graph has the same y-value, or range, for all x values.
As the function's x-values are restricted from 0 to 20, it doesn't affect the y-value because the range would still be the same constant value that the horizontal line is on.
If we go with the assumption that a function described as f(x) = a horizontal line means that f(x) has a constant value for all x in its domain, then the range of f is simply that constant value.
For example, if the function is f(x) = 20 for all 0 ≤ x ≤ 20, then the range is {20}, since f(x) is 20 for all x-values between 0 and 20, inclusive.