# Does the relation represent a function?

Space and AstronomyWRITING IN MATH How can you determine whether a relation represents a function? SOLUTION: **A relation is a function if each element of the domain is paired with exactly one element of the range**. If given a graph, this means that it must pass the vertical line test.

## How do you know if the relation is a function?

A relation is a function only **if it relates each element in its domain to only one element in the range**. When you graph a function, a vertical line will intersect it at only one point.

## Is the relation a function yes or no?

ANSWER: Sample answer: You can determine whether each element of the domain is paired with exactly one element of the range. For example, if given a graph, you could use the vertical line test; **if a vertical line intersects the graph more than once, then the relation that the graph represents is not a function.**

## Which among the relations is not a function?

Examples

A relation which is not a function | A relation that is a function |
---|---|

As we can see duplication in X-values with different y-values, then this relation is not a function. |
As every value of X is different and is associated with only one value of y, this relation is a function |

## Are all function relations?

**All functions are relations**, but not all relations are functions. A function is a relation that for each input, there is only one output. Here are mappings of functions. The domain is the input or the x-value, and the range is the output, or the y-value.

## Which set of relations is a function?

**If every element of a set A is related with one and only one element of another set** then this kind of relation qualifies as a function. A function is a special case of relation where no two ordered pairs can have the same first element. This notation f:X→Y denotes that f is a function from X to Y.

## Why is a function a relation and a relation not a function?

**A function is a relation in which each input has only one output**. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.

## What makes a function not a function?

A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. **They feature at least one value in the domain that corresponds to two or more values in the range**.

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