The Customers

Task

A certain business keeps a database of information about its customers.

1. Let $C$ be the rule which assigns to each customer shown in the table his or her home phone number. Is $C$ a function? Explain your reasoning.

   $\text{Customer Name}$	$\text{Home Phone Number}$
   Heather Baker	3105100091
   Mike London	3105200256
   Sue Green	3234132598
   Bruce Swift	3234132598
   Michelle Metz	2138061124

2. Let $P\,$ be the rule which assigns to each phone number in the table above, the customer name associated with it. Is $P$ a function? Explain your reasoning.
3. Explain why a business would want to use a person's social security number as a way to identify a particular customer instead of their phone number.

IM Commentary

The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context. Instructors might prepare themselves for variations on the problems that the students might wander into (e.g., whether one person could have two home phone numbers) and how such variants affect the correct responses.

Solution

1. $C$ is a function because it assigns to each customer exactly one home phone number.
2. $P$ is not a function because it assigns to the home phone number, 3234132598, more than one customer name: Sue Green and Bruce Swift.
3. A company would want to use social security numbers to identify customers, because not only does each customer have exactly one social security number, but each social security number is associated with exactly one customer.