Definition of a function

Question

Suppose x=1,2 and f(1)=2, f(1)=5, and f(3)=4

 

use the definition of a function to explain why f defined in such a way is not a function.

Answer 1

The relation fails the vertical line test at x=1.   You have two y values that share the same x value.

Answer 2

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

 

In order for a relation to be a function, it can only have one y value for each x value.  In this scenario here we have two different y values for the same x value of 1.  Therefore this relation can not be a function