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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

Campbell University

Oregon State University

McMaster University

Harvey Mudd College

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 determine whether this red graph might be a function or not. So let's take a moment and review what the vertical line test is and what it shows us now. The definition of a function says that every input has exactly one output. Our inputs are our X values. The outputs are the wise. So what this tells us is that every X can Onley be associated with a single Why, in order for this to be a function So if I draw a vertical line on the graph, that vertical line represents an X value. In order for this to be true, for every ex have only one. Why that vertical line can Onley touch my graph and at most one place if it touched in two places, that would mean that my ex value is getting mapped to multiple wise. That is against the definition of a function. So if we have that, we could have a graph, but it's not gonna be a function. So let's take a look at our graph as we slide this vertical line left and right. It's on Lee ever going to touch the graph in at most one place. That means it passes the vertical line test. And, yes, it is a function.

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