Final answer:
The domain and range of the function described, which is a horizontal line at the height of 20, are [0, 20] and {20} respectively. As the function is constant, it neither increases nor decreases, and its range consists of only one number, which is 20. Understanding the domain and range is essential for avoiding calculation errors and for understanding mathematical concepts.
Step-by-step explanation:
Understanding the domain and range of a function that increases or decreases requires analyzing its graph and behavior. By definition, the domain represents all the possible input values (x-values) to which the function assigns an output (y-values). Conversely, the range is the set of all possible outputs that the function can produce.
Considering the function f(x) given for 0 ≤ x ≤ 20, with x being a real number, and the graph of f(x) is a horizontal line at the height of 20. The graph represents a constant function meaning no matter what value of x is within the domain, the output f(x) will always be 20. Therefore, the function mentioned does not truly increase or decrease; instead, it remains constant across its domain.
Based on this information, we can define the domain of this function as the closed interval [0, 20]. The range, however, is a single value, which in this case is the constant value 20. Hence, the range can be expressed as the set containing only the number {20}.
The importance of understanding domain and range is highlighted, as it serves as a guideline to prevent miscalculations and to ensure grasp of the underlying mathematical concepts. Through practice and intuition, students can better anticipate the reasonable domain and range for functions they encounter.