Sure! To identify which function could represent the discrepancy in the diameter of the golf balls, let's break down the problem step-by-step.
### Problem Restatement
1. The standard diameter of a golf ball is \( 42.67 \, \text{mm} \).
2. We need a function that calculates the discrepancy of measured diameters from this standard.
3. The discrepancy in diameter should not exceed \( 0.002 \, \text{mm} \). If it does, production is stopped.
The goal is to find a function \( f(x) \) that represents how far a measured diameter \( x \) is from the standard diameter \( 42.67 \, \text{mm} \).
### Step-by-Step Solution:
1. Understand the Discrepancy Calculation:
- Discrepancy - the absolute difference between the measured diameter \( x \) and the standard \( 42.67 \, \text{mm} \).
- This can be calculated as: \( \lvert 42.67 - x \rvert \).
2. Formulate the Problem in Terms of the Discrepancy Function:
- We need to find \( f(x) \) such that \( f(x) = \lvert 42.67 - x \rvert \).
3. Break Down Each Given Function:
- \( f(x) = x - \lvert 42.67 \rvert \):
- This expression is not correct as it simplifies to \( x - 42.67 \), which is not an absolute difference.
- \( f(x) = \lvert x \rvert - 42.67 \):
- This expression also is not correct because it subtracts the standard diameter from the absolute value of \( x \).
- \( f(x) = \lvert 42.67 - x \rvert \):
- This is exactly the discrepancy calculation required. It captures the absolute difference between the measured diameter and the standard.
- \( f(x) = 42.67 - \lvert x \rvert \):
- This expression subtracts the absolute value of \( x \) from the standard diameter, which is not correct as the discrepancy function.
### Conclusion
The correct function that represents the discrepancy in the diameter is:
[tex]\[ f(x) = \lvert 42.67 - x \rvert \][/tex]
Thus, the appropriate choice is:
[tex]\[ f(x) = \lvert 42.67 - x \rvert \][/tex]
Hence, we see that the inspector should use this function to ensure the diameters remain within the allowable discrepancy limit of [tex]\( 0.002 \, \text{mm} \)[/tex].
