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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

Missouri State University

Oregon State University

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 are being asked to use the vertical line test to determine whether are given graph is or is not a function. So let's take a moment and look at what the vertical line test is and what it shows us to do that we're going to go all the way back to the definition of a function. Ah, function is a group of numbers, you know, that's a pairing of numbers where every input gets mapped to exactly one output. Now our inputs are X values are outputs are wise. So for in a function, every ex gets mapped to exactly one. Why now when I try Aw, a vertical line on the graph like that blue one there. That's a visual representation of this relationship. The line represents a single X value, and I want that xto Onley goto one y like that green dot Right there. If there was a place that I could put that vertical line were intercepted, the graph in more than one place, that would mean that my ex would be being mapped to a variety of different wise. That is contrary to the definition of a function it can Onley Goto one output if it's going to be a function. So let's look at our line here. If I take that blue line and I slide it left and right across my grid, there is nowhere I can put it that will cross that group that graph in more than one place. So every X is indeed only being mapped to a single why it passes the vertical line test. So, yes, it is a function.

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