# What is an even function?

#### short answers for big questions

A function is even when every x value belongs to its domain and the x symmetric has the same image. According to mathematical language it means: f(x) = f(-x) , x in D_f. For those who don't understand the subject, it seems a little confusing. So, I'll explain it better for you to understand.

This graph shows a quadratic function (y=x^2) which is an even function. Here we can notice that both the object 2 and its symmetric have image 4. According to mathematical language: f(2) = f(-2) = 4 . But we have to pay attention, since according to the definition it is not enough to have two symmetric objects with the same image! For a function to be considered even all the objects and the correspondent symmetric must have the same image.

These functions are particularly symmetric regarding the y-axis (O_y). If we fold the sheet vertically, we will notice that the graph, on the left side of the sheet, will lay over the graph on the right side.

## If a function is not even, is it odd?

This is a frequent mistake made by pupils: “if a number is not even, it is obviously odd. So if a function is not even, it is odd for sure.” However, in the case of functions, this is not true. There is a completely different definition concerning an odd function, that will be explained in another topic.

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