Let's break down the solution step by step:
1. Determine the input, or independent variable:
- In the function [tex]\( f(x) = 10 \cdot x^3 \)[/tex], the variable [tex]\( x \)[/tex] is the input variable, which means it is the independent variable.
- So, the input, or independent variable, is [tex]\( x \)[/tex].
2. Determine the output, or dependent variable or quantity:
- In the same function [tex]\( f(x) = 10 \cdot x^3 \)[/tex], [tex]\( f(x) \)[/tex] represents the output variable, which means it is the dependent variable because its value depends on the input [tex]\( x \)[/tex].
- Therefore, the output, or dependent variable, is [tex]\( f(x) \)[/tex].
3. Interpret the notation [tex]\( f(2) \)[/tex]:
- The notation [tex]\( f(2) \)[/tex] refers to the value of the function when [tex]\( x = 2 \)[/tex].
- In other words, [tex]\( f(2) \)[/tex] means the output (y-value) when [tex]\( x = 2 \)[/tex].
4. Evaluate [tex]\( f(2) \)[/tex]:
- To find [tex]\( f(2) \)[/tex] for the function [tex]\( f(x) = 10 \cdot x^3 \)[/tex], substitute [tex]\( x \)[/tex] with 2 in the function.
- So, [tex]\( f(2) = 10 \cdot (2)^3 = 10 \cdot 8 = 80 \)[/tex].
- Therefore, [tex]\( f(2) = 80 \)[/tex].
Here are the answers to the questions:
- The input, or independent variable, is [tex]\( x \)[/tex].
- The output, or dependent variable or quantity, is [tex]\( f(x) \)[/tex].
- The notation [tex]\( f(2) \)[/tex] means the output (y-value) when [tex]\( x = 2 \)[/tex].
- [tex]\( f(2) = 80 \)[/tex].
