The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0.002 mm. Which function could represent this situation?
A. f(x ) = x – |42.67|
B. f(x ) = |x| – 42.67
C. f(x ) = |42.67 – x|
D. f(x ) = 42.67 – |x|
Answer: The correct answer is f(x ) = |42.67 – x|
Production will be stopped if the difference in diameter is greater than 0.002 mm.
This difference can mean that the golf ball has a diameter more than 0.002 larger than 42.67 mm, or a diameter more than 0.002 smaller than 42.67. This is the reason for using an absolute value function.
The absolute value represents the distance a number is from 0. For this function, we would want only the values where the function is less than 0.002.