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# Even and Odd Functions

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In this lesson, we will learn how to determine if a function is even, odd, or neither. We will begin by discussing how to determine if a graph is symmetric with respect to the y-axis. This occurs when we can replace x with -x and obtain the same equation. When a function has this property, f(-x) = f(x), we can say this is an even function. Additionally, we will see that when y can be replaced with -y and we have the same equation, the graph is symmetric with respect to the x-axis. A graph that is symmetric with respect to the x-axis will fail the vertical line test, therefore, it is not a function. For a given x value, it will have a y and -y that is associated. Lastly, we will discuss a graph that is symmetric with respect to the origin. For this graph, we can replace x with -x and y with -y and obtain the same equation. A function with this property is known as an odd function. We can show this as:

f(-x) = -f(x) or -f(-x) = f(x)

f(-x) = -f(x) or -f(-x) = f(x)

Even and Odd Functions:

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