Does This Graph Show A Function? How To Know

Introduction

When you first start learning about functions in mathematics, one of the key concepts you need to understand is how to determine whether a graph represents a function or not. In this article, we will explore the different ways to determine if a graph represents a function, and explain the reasoning behind these methods.

What is a Function?

A function is a mathematical relationship between two variables, where each input (x) corresponds to exactly one output (y). A graph that represents a function will pass the vertical line test, which means that no vertical line intersects the graph more than once.

Vertical Line Test

The vertical line test is a graphical way to determine whether a curve is a graph of a function or not. If any vertical line intersects the curve at more than one point, then the curve is not the graph of a function.

Examples of Function Graphs

Let’s take a look at some examples of graphs that represent functions.

Example 1: The graph of y = x^2 is a function because every vertical line intersects the graph at most once, as shown below:

Example 2: The graph of y = sin(x) is also a function, because every vertical line intersects the graph at most once:

Examples of Non-Function Graphs

Now let’s look at some examples of graphs that do not represent functions.

Example 1: The graph of a circle is not a function, because there are vertical lines that intersect the graph at more than one point:

Example 2: The graph of a line that is not vertical is a function, but the graph of a vertical line is not a function, because a vertical line intersects the x-axis at every point:

Other Ways to Check for Functions

In addition to the vertical line test, there are other ways to determine whether a graph represents a function or not. One of these methods is the horizontal line test, which involves checking whether every horizontal line intersects the graph at most once.

Conclusion

In conclusion, determining whether a graph represents a function or not is an important skill in mathematics. By using the vertical line test and other methods, you can quickly determine whether a graph represents a function or not. Remember that a function is a mathematical relationship between two variables, where each input corresponds to exactly one output.