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When working with inverses, what is a function, a relation and what are the requirements for these to exist? (I know it's the vertical and horizontal line test but what is this?)
Thanks


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Generally, a function is a graph that only has one y-value for any value of x. This can be tested using the vertical line test. If you draw a vertical line, which represents a value of x, there should always only be a maximum of 1 point where it crosses over the graph.

A relation is simply any relationship between y and x with no constraints. A function is a type of relation.

In the context of inverses, a function (one y value per any x value) only has an inverse function if there it also passes the horizontal line test (one x value for any y value). This is because an inverse is swapping the x and the y. So if you want your inverse to be a function (one y for every x) you need to make sure the original graph only has one x for every y.


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So basically a relation can contain any relationship between x and y, and in this case a function has a relationship between one x for one y value hence it is considered a relation?
Yes, it is still a relation. (Just like how a square is still a rectangle technically)