The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 8.1: Determining if a Relation Is a Function

A function is a relation if each value in the domain is paired with exactly one member of the

range. Students often incorrectly believe that each member of the range must be paired with

exactly one member of the domain.

1. Explain that a relation is any set of ordered pairs. A function is a special type of relation.
   Emphasize that each member of the domain must be assigned exactly one member of the
   range and each member of the range must be assigned at least one member of the domain.


2. To illustrate the meaning of exactly one, offer this example. A group of three
   girls—Brittany, Rachel, and Inez—represent the domain. A group of three boys—Roberto,
   John, and Tyrone—represent the range. Both groups go to the mall. While shopping,
   Brittany sees Roberto, Rachel sees John, and Inez sees Tyrone. This is an example of each
   member of the domain being paired with exactly one member of the range. Point out that it
   does not matter if, while shopping, John sees Brittany or Inez, or that Tyrone sees Brittany
   or Rachel. Each member of the domain was paired with exactly one member of the range.


3. Review the information and examples on the worksheet with your students. Discuss the def-
   inition of a function and emphasize that ‘‘exactly one’’ means ‘‘one and only one’’ (not two or
   more). ‘‘At least one’’ means ‘‘one or more.’’ Make sure that your students understand why or
   why not a relation is a function.

EXTRA HELP:

Always consider thex-values first. Be sure that each value ofxis paired with exactly oney-value.

Looking at they-values first leads to confusion.

ANSWER KEY:

(1)Function (2)Not a function (1 is paired with 1, 2, 3,

and 4.)

(3)Function (4)Not a function (2 is paired with 4 and−4.)

(5)Not a function (3 is paired with 2 and−2,

and 4 is paired with 15 and−15.)

(6)Function

(7)Not a function (2 is paired with 0, 4, and

−4.)

(8)Function

(9)Not a function (−4 is paired with 2 and 4,

and 0 is paired with 3 and 5.)

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(Challenge)Answers may vary. (1, 5), (2, 6), (3, 7), (4, 8) is one example.

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274 THE ALGEBRA TEACHER’S GUIDE