Identify functions

Learning Objectives Define a mathematical function in their own words. Distinguish between a relation and a function. Identify functions represented by sets of ordered pairs. Identify functions represented by tables of values. Apply the Vertical Line Test to identify functions from graphs. Explain why a given relation is or is not a function. Ever wondered how a vending machine knows exactly what snack to give you when you press a button? 🍫 It's all about a special kind of relationship called a function! In this lesson, you'll discover what makes a relationship a 'function' in mathematics. You'll learn how to identify functions when they're shown as ordered pairs, tables, or graphs, and understand why this concept is fundamental to solving man...

TermDefinitionExample RelationA set of ordered pairs that shows a connection or relationship between an input and an output.{ (1, 2), (2, 4), (3, 6) } FunctionA special type of relation where each input (x-value) has exactly one output (y-value). No input can have more than one output.The relation { (1, 2), (2, 4), (3, 6) } is a function because each x-value has only one y-value. Input (Domain)The set of all possible x-values (or independent values) in a relation or function. These are the values you put into the relationship.In { (1, 2), (2, 4), (3, 6) }, the inputs (domain) are {1, 2, 3}. Output (Range)The set of all possible y-values (or dependent values) in a relation or function. These are the results you get from the relationship.In { (1, 2), (2, 4), (3, 6) }, the outputs (range) ar...

The Function Rule (Input-Output) For a relation to be a function, every input (x-value) must correspond to exactly one output (y-value). This is the fundamental definition. If you find an input value that appears more than once with *different* output values, it's not a function. If an input repeats with the *same* output, it's still a function (e.g., (1,2) and (1,2) is fine, but (1,2) and (1,3) is not). Vertical Line Test (for Graphs) A graph represents a function if and only if no vertical line intersects the graph at more than one point. Imagine drawing vertical lines all across the graph. If even one of these lines touches the graph in two or more places, then that x-value (input) has multiple y-values (outputs), meaning it's not a function. Table/Mapp...