Identifying Functions from Relations: Testing Vertical Line Test Criteria

Published on March 19, 2026

Functions

Determine which relations, including an equation, a set of ordered pairs, and descriptive rules, represent y as a function of x by checking for unique y-values for each x-value.

Question

which relations represent y as a function of x which do not (2,4),(2,6),(4,4),(4,6) 5x-4y=-20 for each value of x the value of y is double the value of x for each value of the value of y is 0

Answer

The user has presented a list of potential relations and asked which of them represent

as a function of

A relation represents

as a function of

if and only if for every input value of

, there is exactly one output value of

. This is known as the vertical line test for a graph, or simply checking that no two ordered pairs

and

exist in the relation where

Let’s analyze each given relation:

1. The set of ordered pairs

This relation contains the following ordered pairs:

When , can be or .
When , can be or .

Since there are two different

values (

and

) corresponding to the single

value of

, this relation does not represent

as a function of

2. The equation

To determine if this is a function, we solve for

in terms of

Subtract

from both sides:

Divide both sides by

Since this equation yields exactly one value of

for every value of

, this relation does represent

as a function of

3. "for each value of the value of is double the value of "

This statement describes a relationship where

is defined based on

. If

is double

, then:

For any given

, there is only one value for

(namely

). Therefore, this relation does represent

as a function of

4. "for each value of the value of is "

This statement is slightly ambiguous in its phrasing ("for each value of the value of

"). Assuming the intended meaning is: “For each value of

, the value of

,” the relation is:

For any given

is uniquely determined to be

. Therefore, this relation does represent

as a function of

(If the statement meant “for each value of

, the value of

,” this would imply the relation is just the set of points

. In this standard interpretation, it is still a function of

The relations that represent

as a function of

are:

(based on the description "for each value of the value of is double the value of ")
(based on the interpretation of the last statement)

The relation that does not represent

as a function of

is:

The question asks “which relations represent

as a function of

which do not [list the set of points]”. This phrasing is slightly confusing. It seems to ask for the functions among the provided options, excluding the one that is explicitly not a function (the set of points).

If the question is interpreted as "Identify all relations listed that ARE functions of

The functions are: