Final answer:
The domain of the constant function f(x) = 1 for 0 ≤ x ≤ 20 is [0, 20], and the range is {1} since the function outputs a constant value of 1 across the entire domain.
Step-by-step explanation:
When finding the domain and range of a function, we are identifying the set of all possible inputs (x-values) and the resulting set of potential outputs (y-values), respectively. For a function described as a horizontal line, such as f(x) = 1 for 0 ≤ x ≤ 20, the domain is the interval from 0 to 20, inclusive. Because the function is a constant function, the range is simply the value that the function outputs for every input in the domain, which in this case is 1.
Domain of f(x) = 1 when 0 ≤ x ≤ 20:
- Since the function is defined for all x-values between 0 and 20, the domain is [0, 20].
Range of f(x) = 1 when 0 ≤ x ≤ 20:
- The output of the function is a constant, the range is simply {1}, since no matter the input value between 0 and 20, the output is always 1.
The graph of this function would be a straight horizontal line at y = 1 between x = 0 and x = 20.