Question

Can you tell me what would make something a function vs. what is not a function?

Answer 1

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function

Answer 2

fails the vertical line test: not a function

Explanation:

You want to know how to tell if a relation is a function or not.

Relation

A relation is a map between values of the independent variable (input, x) and values of the dependent variable (output, y). Such a map can be represented many ways, including a table, graph, set of ordered pairs, dual number lines, or even a diagram showing inputs and outputs. The attachment shows such a diagram.

A relation does not need to be between numbers. Tokens of any kind can be used for input and output identifiers.

Function

A function is a relation in which each input corresponds (maps) to exactly one output.

The relation shown on the left of the attachment is not a function because the first (top) input item (A) maps to more than one output item (B).

When a relation is expressed as ordered pairs (x, y) or a table, it will be a function if and only if no x-value is repeated.

When a relation is expressed as a graph, it will be a function if and only if no vertical line intersects more than one point on the graph. (This is the "vertical line test.")