# A teacher polled her kindergarten class to see what each student's favorite color was: Color Number of Students Red 5 Blue 7 Green 3 Yellow 2 Orange 1 Purple 5 Does the...

A teacher polled her kindergarten class to see what each student's favorite color was:

Color Number of Students Red 5 Blue 7 Green 3 Yellow 2 Orange 1 Purple 5

Does the relation's* inverse* represent a function? Why or why not?

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Expert Answers

baxthum8 | Certified Educator

Assuming color represents the relations input and the number of students represents the output, the relations inverse would not be a function. To determine switch the inputs and outputs of a relation to find its inverse, therefore we would have 5, red ; 7, blue; 3, green; 2, yellow; 1, orange, and 5, purple.

Because this relation now has 2 outputs for 5, that being red and yellow, this would not represent a function. In order to be a function, each input must have exactly one unique output.