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# Relations and Functions

## Comparison of two or more sets of values, and cases where input corresponds with exactly one output.

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Practice Relations and Functions
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Defining Relations and Functions

### Vocabulary Language: English

dependent variable

dependent variable

The dependent variable is the output variable in an equation or function, commonly represented by $y$ or $f(x)$.
independent variable

independent variable

The independent variable is the input variable in an equation or function, commonly represented by $x$.
input

input

The input of a function is the value on which the function is performed (commonly the $x$ value).
Output

Output

The output of a function is the result of the operations performed on the independent variable (commonly $x$). The output values are commonly the values of $y$ or $f(x)$.
Relation

Relation

A relation is any set of ordered pairs $(x, y)$. A relation can have more than one output for a given input.
Vertical Line Test

Vertical Line Test

The vertical line test says that if a vertical line drawn anywhere through the graph of a relation intersects the relation in more than one location, then the relation is not a function.