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Use the vertical line test to determine if the given graph may represent a function.

Is

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Use the vertical line test…

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for this problem. We have been asked to use the vertical line test to examine our graph and decide whether it is or is not a function. So before we do that, let's review what the vertical line test is and what it shows. Us and Thio really understand it. We're going to go all the way back to the definition of a function. A function says. Every input into the function gets mapped to exactly one output. Now our inputs are X values. Outputs are y values. So for a function, every x can Onley go toe one white House have exactly one Why as an output. So if I draw a vertical line on our graph like this blue line here, that's a visual representation of this relationship. The blue line represents one X value and I wanted toe Onley map to a single. Why, Yeah, that's at Greenpoint. I just do on the graph. If I can draw a vertical line on my graph somewhere and have it crossed in more than one place, that means that my the same X could be going toe multiple y values that is against the definition of a function. I want every xto Onley have one. Why the vertical line can Onley cross in one place. So for the graph we've been given, if we slide that line left and right across there is nowhere I can put it where it will cross the graph in more than one place. So it passes the vertical line test. And yes, it is a function.

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