To answer the question, we need to analyze the notation [tex]\( s(x) \)[/tex] in the context of functions and how this notation is generally understood in mathematics.
1. Understanding Functions:
- The notation [tex]\( s(x) \)[/tex] is commonly used to represent a function named [tex]\( s \)[/tex] that takes an input [tex]\( x \)[/tex].
- In this context, [tex]\( s(x) \)[/tex] signifies the output of the function [tex]\( s \)[/tex] when the input is [tex]\( x \)[/tex].
2. Option Analysis:
- Option A: "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 statement is incorrect. Here, [tex]\( x \)[/tex] is the input variable, and [tex]\( s(x) \)[/tex] is the output. The input does not depend on the output.
- Option B: "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 statement is correct. The entire concept of functions is based on the idea that the output (value of the function) depends on its input. Thus, [tex]\( s(x) \)[/tex] depends on [tex]\( x \)[/tex].
- Option C: "There is not enough information to answer this question." This is incorrect because the notation [tex]\( s(x) \)[/tex] provides clear information that [tex]\( s \)[/tex] is a function of [tex]\( x \)[/tex].
- Option D: "The value found when [tex]\( s \)[/tex] is multiplied by the value [tex]\( x \)[/tex]." This statement is incorrect. The notation [tex]\( s(x) \)[/tex] does not indicate multiplication but rather denotes [tex]\( s \)[/tex] as a function applied to [tex]\( x \)[/tex].
3. Conclusion:
- Based on the analysis of functions and the given options, the correct answer is Option B: "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]."
Therefore, the correct answer is:
B. 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].
