Final answer:
The domain of the horizontal line function for 0 ≤ x ≤ 20 is [0, 20]. The range would be a single constant value, which is the y-value at which the horizontal line is situated. To specify the range, the value of the constant would be needed.
Step-by-step explanation:
The question pertains to finding the domain and range of a relation given in interval notation. The function described is a horizontal line, where f(x) is defined for 0 ≤ x ≤ 20. This means the function takes as input any real number between 0 and 20, inclusive of 0 and 20. Since the graph is a horizontal line, f(x) does not change with x, which implies that the range is a constant value.
Therefore, the domain of the given function, expressed in interval notation, would be [0, 20] since it includes all x-values from 0 to 20. The range, on the other hand, since it is a horizontal line and the value of f(x) remains constant, would simply be the value on the y-axis that the horizontal line crosses, expressed as [c, c] where c is the constant value of f(x). However, there is not enough information to determine the exact value of c without additional context. It is clear, however, that the answer keys a), b), and d) do not represent the correct range because they imply variability in the value of f(x), which contradicts the description of a horizontal line.