# Examples of Mathematical Functions

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A mathematical function is a relation in which each element of the domain tends to be x-coordinates and is paired with an element of the range. Learn about what must happen before a relation can be called a function with help from a math teacher in this free video on math help and functions.

Part of the Video Series: Algebra & Math Help
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## Video Transcript

So what are some examples of mathematical functions? Hi, I'm Jimmy Chang. I've been teaching college mathematics for over nine years now. And before we can do some examples of mathematical functions. Let's just make sure that we understand the definition of a mathematical function. Now one definition is, it's a relation where each element of the domain. In other words, domain tends to be X-coordinates. Is paired with an element of the range. For example Y-coordinates. Now typically, what ends up happening is you have a lot of ordered pairs. Generally of X, Y coordinates. But there is one additional condition that must be met. Before you can call a relation a function. No two distinct pairs can be, can have the same X coordinate. In other words, you cannot have two pairs sharing the same X coordinates. So for example, you cannot have a pair of 1,2 and 1,3 in a function. They cannot share the same X coordinate. Now typically a lot of functions have the notation F. Sometimes G, H, so on and so forth are used. But F is the predominant letter for function. F for function. Go figure. And typically speaking X is generally the most widely used letter for, the variables are used in this function. Now here are some brief examples of mathematical functions. Suppose you have F of X equals to X. Now the graph of that function tends to be a line. Now if we have a function F of X equals X squared. If you make a table of points, you'll find out that it is, that a way, looks like a happy face. This is known as a, also a Parabola. You also have F of X equals to absolute value of X. You can actually grab absolute values. And you'll find that the standard absolute value function. Tends to be that of a V shape graph. and then you have F of X equals X cubed. Which if you make a table. You'll find that it is kind of, like a snake looking graph. But we'll see these mathematical functions over and over again. Not just in Algebra. But also the advanced course like Precalculus and Calculus. So, I'm Jimmy Chang. And there are some examples of mathematical functions.

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