Which is not a function?

A function is a relation if each input value corresponds exactly to one output value. In other words, a relation is considered a function if there are no repeating x-values in a given relation.

( 1 ) Table of values: A Function

The given relation is a function since each x-coordinate has its own corresponding y-coordinate, and that there are no repeating x-values in the table.

(2) Absolute value graph: A Function

This graph represents a function because each x-value corresponds exactly to one y-coordinate. Another way to prove this is to perform the Vertical Line Test (VLT). In order to perform the VLT, simply draw vertical lines across the graph to see whether each vertical line crosses the graph more than once. Attached is an edited screenshot where I performed the VLT. It shows that there is only one red dot in each vertical line drawn. Thus, the given graph is a function.

(3) 3x + 2y = 4: A Function

This linear equation in standard form represents a function, as each x-value in its solution corresponds exactly to one y-value.

(4) Mapping of numbers to letters: Not a Function

In the given diagram of a correspondence, or mapping, of the first set (numbers) to the second set (letters), it shows that the number 2 corresponds to two output values: A and B. Therefore, this given relation is not a function.