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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

Campbell 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 have been asked to look at this red graph, and we want to use the vertical line test to determine whether this red graph might be a function in order to do that. Let's review what the vertical line test shows us and why it works. The definition of a function says every input has exactly one output. Okay, now inputs are exes. Outputs are wise. So this is saying that every X value good it gets mapped to exactly one. Why now, when I put a vertical line on my graph like that one right there that is representing a single X value for this function definition to be true that X can Onley be associated with one. Why? Which means it can Onley cross my graph in one place in order for this to be a function and as I slide that blue line left and right, that has to be true for every single point on my red graph. If there's any place where my blue line crosses more than once, that means my ex value is being matched to more than one. Why we can't have that. That's not you know if we have that it violates the definition of a function, so we might have a nice graph. But it's not a function in that case now for our graph here. As I move that blue line, there is nowhere that I can put it that will cross this red line more than once. So each X really does Onley have one? Why it passes the vertical line test and yes, it is a function.

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