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? f(x ) = x – |42. 67| f(x ) = |x| – 42. 67 f(x ) = |42. 67 – x| f(x ) = 42. 67 – |x|.

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ashishdwivedilVT ashishdwivedilVT · Answer 1 · 2022-03-17T07:07:54+01:00

Using function theory, the function that could represent this situation is

f(x) = |42. 67 – x| .

It is given that

The standard diameter of the golf ball = is 42.67

Allowable discrepancy = ±0.002

So upper limit of diameter = 42.672

The lower limit of diameter = 42.668

We need a function that can help in finding a discrepancy.

A function is a rule which determines the relation between two variables.

The correct function that could represent this situation will be

f(x ) = |42. 67 – x|

Where x is the diameter of the ball produced.

For example, if a ball of diameter 42.665 is produced

f(x) = |42. 67 – x|

f(42.665) = |42. 67 – 42.670| = 0.005 which is more than the permitted tolerance i.e 0.002.

So, one can easily decide whether to stop production or not.

Therefore, the function that could represent this situation is

f(x) = |42. 67 – x| .

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