To understand what [tex]\( s(x) \)[/tex] represents in the notation [tex]\( s(x)=\ldots \)[/tex], let’s break down the components.
1. Function Notation:
- In mathematics, the notation [tex]\( s(x) \)[/tex] is standard for representing a function named [tex]\( s \)[/tex] evaluated at [tex]\( x \)[/tex].
- The [tex]\( s(x) \)[/tex] is often read as " [tex]\( s \)[/tex] of [tex]\( x \)[/tex]".
- This notation implies that [tex]\( s \)[/tex] is a rule or relationship that assigns to every element [tex]\( x \)[/tex] in its domain exactly one element in its range.
2. Analysis of Each Option:
- Option A: "The value found when [tex]\( s \)[/tex] is multiplied by the value [tex]\( x \)[/tex]." This is incorrect. [tex]\( s(x) \)[/tex] represents the output of the function [tex]\( s \)[/tex] when applied to [tex]\( x \)[/tex], not the product of [tex]\( s \)[/tex] and [tex]\( x \)[/tex].
- Option B: "The value of [tex]\( x \)[/tex] depends on the value of [tex]\( s(x) \)[/tex], since [tex]\( x \)[/tex] is a function of [tex]\( s \)[/tex]." This is incorrect. It reverses the dependence; in function notation, the output [tex]\( s(x) \)[/tex] depends on the input [tex]\( x \)[/tex].
- Option C: "The value of [tex]\( s(x) \)[/tex] depends on the value of [tex]\( x \)[/tex], since [tex]\( s \)[/tex] is a function of [tex]\( x \)[/tex]." This is correct. This option accurately describes the relationship in function notation.
- Option D: "There is not enough information to answer this question." This is incorrect. There is enough information provided by the notation [tex]\( s(x) \)[/tex] to determine the correct relationship.
Therefore, the correct answer is:
C. The value of [tex]\( s(x) \)[/tex] depends on the value of [tex]\( x \)[/tex], since [tex]\( s \)[/tex] is a function of [tex]\( x \)[/tex].
