Let's address the question step by step.
1. Interpretation of \( x \) and \( g(x) \):
- In the context of the problem, \( x \) represents the number of birdhouses built by the carpenter.
- The function \( g(x) \) represents the number of wood pieces used to build the birdhouses.
2. Given Pair \((100, 2)\):
- We are given the pair \((100, 2)\).
- Here, \( x = 100 \) and \( g(x) = 2 \).
3. Does \((100, 2)\) Make Sense?:
- For \( x = 100 \), \( g(x) = 2 \).
- This means that if the carpenter builds 100 birdhouses, only 2 pieces of wood are used in total.
4. Analyzing the Practicality:
- It is important to consider whether using only 2 pieces of wood to build 100 birdhouses is feasible.
- Typically, building a single birdhouse would require multiple pieces of wood, and certainly more than 2 pieces in total for 100 birdhouses.
- Therefore, the given pair \((100, 2)\) seems impractical for real-world scenarios, as using only 2 pieces of wood for 100 birdhouses seems highly unlikely.
### What Does \( x \) Represent?
From our detailed analysis:
- \( x \) represents the number of birdhouses built.
### What Does \( g(x) \) Represent?
From our detailed analysis:
- \( g(x) \) represents the number of wood pieces used to build the birdhouses.
### Conclusion
Given the practical consideration, while the pair \((100, 2)\) describes a mathematical relationship, it is not realistic for building birdhouses. Nonetheless, this is the interpretation of the given problem.
So, summarizing:
- \( x \) represents the number of birdhouses built.
- [tex]\( g(x) \)[/tex] represents the number of wood pieces used to build the birdhouses.
