Certainly! Let's explore the given function [tex]\( f(x) = 10 - x^3 \)[/tex] step-by-step.
### 1. Identifying the Input or Independent Variable
For the function [tex]\( f(x) = 10 - x^3 \)[/tex]:
- The input, or independent variable, is [tex]\( x \)[/tex].
### 2. Identifying the Output or Dependent Variable
For the function [tex]\( f(x) = 10 - x^3 \)[/tex]:
- The output, or dependent variable, is [tex]\( f(x) \)[/tex].
### 3. Understanding the Notation [tex]\( f(2) \)[/tex]
The notation [tex]\( f(2) \)[/tex] refers to:
- The output, or the [tex]\( y \)[/tex]-value, when the input [tex]\( x \)[/tex] is equal to 2.
### 4. Evaluating [tex]\( f(2) \)[/tex]
To evaluate [tex]\( f(2) \)[/tex]:
- We substitute [tex]\( x \)[/tex] with 2 in the function [tex]\( f(x) = 10 - x^3 \)[/tex].
Substituting [tex]\( x = 2 \)[/tex] in the function:
[tex]\[ f(2) = 10 - (2)^3 \][/tex]
[tex]\[ f(2) = 10 - 8 \][/tex]
[tex]\[ f(2) = 2 \][/tex]
Therefore, [tex]\( f(2) \)[/tex] evaluates to [tex]\( 2 \)[/tex].
In summary:
- The input, or independent variable, is [tex]\( x \)[/tex].
- The output, or dependent variable, is [tex]\( f(x) \)[/tex].
- The notation [tex]\( f(2) \)[/tex] means the output when [tex]\( x = 2 \)[/tex].
- Evaluating [tex]\( f(2) \)[/tex], we get [tex]\( f(2) = 2 \)[/tex].
