# Relations and Functions

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A series of free Basic Algebra Lessons.

In this lesson, we will learn

• about relations and how to determine whether a relation is a function
• about the function notation

### Relations and Determining Whether a Relation is a Function

Understanding relations (defined as a set of inputs and corresponding outputs) is an important step to learning what makes a function. A function is a specific relation, and determining whether a relation is a function is a skill necessary for knowing what we can graph. Determining whether a relation is a function involves making sure that for every input there is only one output.

How to determine if a relation is a function?
This video explains how to determine if you have a function. It includes the vertical line test.

### Function Notation

Throughout mathematics, we find function notation. Function notation is a way to write functions that is easy to read and understand. Functions have dependent and independent variables, and when we use function notation the independent variable is commonly x, and the dependent variable is F(x). In order to write a relation or equation using function notation, we first determine whether the relation is a function.

Function Notation - A basic description of function notation and a few examples involving function notation. Using function notation.
What is f(x)? It is a different way of writing "y" in equations, but it's much more useful. The meaning and necessity of function notation, what it looks like, and how to use it.

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