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The Customers


Alignments to Content Standards: 8.F.A.1 F-IF.A.1

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.

Michael says:

over 1 year

Is it so clear that P isn't a function? What if the range of P is sets of people living under an address? That would make a perfectly fine function, I think.

Evan says:

6 months

The range of P is defined in part (b), "Let P be the rule which assigns to each phone number in the table above, the customer name(s) associated with it." I believe I understand your critique Michael. If we have the output of our function P(phone number) be the list of names associated with that number {name_1, name_2...}, it is a function because there is only one list associated with each number. One could write a computer function to perform this process... Is that an acceptable response from a student on this task?

If the range is defined as a single name associated with the number - then we have 2 possible names for one of the numbers and it is not a function. Perhaps we should remove the "(s)" from "name(s)"?

Make it, "Let P be the rule which assigns to each phone number in the table above, the customer name associated with it."

Seems like an improvement to the task? Am I off-base here?

Bill says:

6 months

This does seem like an improvement, thanks.

Jennifer wright says:

over 5 years

Tis would be a good opening