Identify functions vertical line test

Learning Objectives Define a relation and a function. Explain the purpose and procedure of the vertical line test. Apply the vertical line test to a given graph to determine if it represents a function. Distinguish between graphs of functions and non-functions, including linear equations. Connect the outcome of the vertical line test to the definition of a function. Analyze the graphs of individual equations within a system to verify they are functions. Can a person be in two different places at the exact same time? 🤔 The vertical line test helps us check for impossible situations like this on a graph! In this tutorial, you will learn a simple visual method called the Vertical Line Test to quickly identify if a graph represents a function. This is a foundational skill for...

TermDefinitionExample RelationAny set of ordered pairs (x, y). It describes a relationship between two sets of values, the inputs and the outputs.The set {(1, 5), (2, 10), (2, 11), (3, 15)} 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 {(1, 5), (2, 10), (3, 15)} is a function. The previous example is not, because the input 2 has two different outputs (10 and 11). DomainThe set of all possible input values (x-coordinates) for a relation or function.For the function {(1, 5), (2, 10), (3, 15)}, the domain is {1, 2, 3}. RangeThe set of all possible output values (y-coordinates) for a relation or function.For the function {(1, 5), (2, 10), (3, 15)}, the range...

Definition of a Function For a relation to be a function, for every x in the domain, there must be exactly one y in the range. This is the fundamental principle that the vertical line test visually checks. If an x-value has more than one y-value, the relation is not a function. The Vertical Line Test A graph represents a function if and only if no vertical line can be drawn that intersects the graph at more than one point. Use this test by imagining or drawing a vertical line and sweeping it across the entire graph from left to right. If the line ever touches the graph in two or more places simultaneously, the graph does not represent a function. Equation of a Vertical Line x = c This is the general equation for a vertical line, where 'c' is the x-value at...