To determine the input or independent variable of the function [tex]\( f(x) = 10 - x^3 \)[/tex], let's analyze the elements given in the function and their roles.
### Steps:
1. Understanding the Function:
- In the function [tex]\( f(x) \)[/tex], the notation [tex]\( f(x) \)[/tex] implies that [tex]\( f \)[/tex] is a function of [tex]\( x \)[/tex].
- The notation [tex]\( f(x) \)[/tex] reads as "f of x," which means the function's output relies on the input [tex]\( x \)[/tex].
2. Identify the Components:
- [tex]\( f(x) \)[/tex] represents the output of the function. It is typically dependent on the input value and is not an independent variable itself.
- [tex]\( x \)[/tex] is inside the parentheses directly after the function notation [tex]\( f \)[/tex], which signifies that [tex]\( x \)[/tex] is the variable we are plugging into the function. Therefore, [tex]\( x \)[/tex] is the independent variable.
- [tex]\( y \)[/tex] is not explicitly mentioned in the given function definition. It is a common notation for an output variable in the y-axis in graphing contexts, but since it's not part of our function definition [tex]\( f(x) = 10 - x^3 \)[/tex], it is irrelevant to the identification of the independent variable here.
3. Conclusion:
- Since [tex]\( x \)[/tex] is the variable that we provide as an input to the function and it determines the output, [tex]\( x \)[/tex] is the independent variable.
Thus, the input or independent variable for the function [tex]\( f(x) = 10 - x^3 \)[/tex] is [tex]\( x \)[/tex].
