Learn calculus 1 part 1

Definition of a function A function f from a set of elements X to a set of elements Y is a rule that assigns to each element x in X exactly one element y in Y .

There are lots of ways to visualize or picture a function in your head. You can think of it as a machine accepting inputs and shooting out outputs, or a set of ordered pairs, or whatever way you come up with. However, by far the most important way to visualize a function is through its graph. By looking at a graph in the xy-plane we can usually find the domain and range of the graph, discover asymptotes, and know whether or not the graph is actually a function.

Even and odd functions have properties that can be useful in different contexts. The most basic one is that for an even function if you know f(x), you know f(-x). Similarly for odd functions, if you know g(x), you know -g(x). Put more plainly, the functions have a symmetry that allows you to find any negative value if you know the positive value or vice versa.

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.

In mathematics, even functions and odd functions are functions that satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series.