Final answer:
The value of s(x) depends on the value of x, since s is a function of x. It denotes a rule that maps every x to a corresponding value. This concept is fundamental for graphing functions and understanding the arbitrary nature of algebraic symbols.
Step-by-step explanation:
In the notation s(X), what does s(x) represent? The correct answer to this question is D. The value of s(x) depends on the value of x, since s is a function of x. In mathematics, functions are relationships between two sets that assign to each element of the first set exactly one element of the second set. In this case, the first set consists of the possible values for x, and s represents the rule that transforms each x into a corresponding value s(x).
Understanding this concept is crucial for graphing functions, where you plot (x, y) data pairs and see how the value of y changes as a function of x. This notation also emphasizes that symbols like x or s are arbitrary placeholders and that in an algebraic equation, choosing different symbols without altering the structure of the equation does not change the meaning. Such substitution must be done consistently to maintain the equation's integrity.