Identify functions

Learning Objectives Define a relation and a function. Distinguish between a relation that is a function and one that is not. By the end of a this lesson, students will be able to identify a function from a set of ordered pairs, a table, and a mapping diagram. Apply the Vertical Line Test to determine if a graph represents a function. Determine the domain and range of a given relation. Explain why a relation is or is not a function using mathematical reasoning. Have you ever pressed a button on a vending machine and gotten two different snacks at once? 🤔 Probably not! That's because vending machines work like a special mathematical relationship called a function. In this tutorial, you will learn the difference between a 'relation' and a 'function',...

TermDefinitionExample RelationAny set of ordered pairs, (x, y). It shows a relationship between two sets of values.The set R = {(1, 2), (2, 4), (3, 6), (1, 5)} is a relation. FunctionA special type of relation where every input (x-value) is paired with exactly one output (y-value). No x-value can be repeated with a different y-value.The set F = {(1, 2), (2, 4), (3, 6), (4, 8)} is a function because each x-value has only one corresponding y-value. DomainThe set of all possible input values (the x-coordinates) in a relation.For the relation R = {(1, 2), (2, 4), (3, 6)}, the domain is {1, 2, 3}. RangeThe set of all possible output values (the y-coordinates) in a relation.For the relation R = {(1, 2), (2, 4), (3, 6)}, the range is {2, 4, 6}. Mapping DiagramA visual way to show how the element...

The Function Rule A relation is a function if for every input x, there is exactly one output y. Formally, if (x, y_1) and (x, y_2) are in the relation, then it must be that y_1 = y_2. Use this rule when you are given a set of ordered pairs, a table, or a mapping diagram. Check if any x-value is paired with more than one unique y-value. If it is, the relation is not a function. The Vertical Line Test A graph represents a function if and only if no vertical line intersects the graph at more than one point. Use this rule when you are given a graph. Imagine sliding a vertical line (like a pencil held straight up and down) across the graph from left to right. If the line ever touches the graph in more than one place at the same time, it is not a function.