Final answer:
The function f(x), defined for 0 ≤ x ≤ 20 as a horizontal line, is a constant function within this interval and can be expressed as a piecewise function: f(x) = c for 0 ≤ x ≤ 20, where c is a constant.
Step-by-step explanation:
To write the given function as a piecewise function, consider the description provided. We have a function f(x) that is defined for values of x between 0 and 20, inclusive. The graph of f(x) is mentioned to be a horizontal line, which implies that the value of f(x) does not change with x in this interval. Therefore, f(x) must be a constant function within the domain 0 ≤ x ≤ 20.
The piecewise function for f(x) can be written as follows:
{
f(x) = c, 0 ≤ x ≤ 20
}
where c is the constant value of the function on the horizontal line. Given that only the restriction of the domain is provided and not the specific constant value, we denote it as c. It's important to note that each piece in a piecewise function corresponds to a specific interval, even if, in this case, there is only one interval for the entire domain.