Final answer:
The rule for the given function with a horizontal line is a constant function expressed as f(x) = c. For a horizontal line at y = 20, the rule within the domain 0 ≤ x ≤ 20 is f(x) = 20. Similar rules apply to continuous probability functions and multiplication of fractions.
Step-by-step explanation:
When dealing with the question of determining the rule for a given function, it's important to first understand the nature of the function presented. Since the function f(x) is described as a horizontal line, the value of f(x) does not change with x. This indicates that f(x) is a constant function. In general, for a constant function where the graph is a horizontal line, the rule could be expressed as f(x) = c, where c is a constant.
In the specific example provided, since the graph of f(x) is restricted between the domain 0 ≤ x ≤ 20, we must consider the boundaries given for the function. However, no additional information about the value of f(x) within this range has been provided. Assuming the line continues horizontally within the given domain, the rule for f(x) would simply be f(x) = c, where c is the value where the horizontal line resides on the y-axis. If the line is at y = 20, the function rule would be f(x) = 20 for all values of x in the domain.
The same approach applies to continuous probability functions and multiplication of fractions. For example, the probability P(x) is always zero for a value of x that lies outside the defined range for a continuous probability distribution. So the probability P(x > 15) or P(x = 10) when the domain ends at x = 7 is 0. Similarly, for fractions, the general multiplication rule is to multiply the numerators together and the denominators together (a/b × c/d = ac/bd).