函数在数学中为两集合间的一种对应关系：输入值集合中的每项元素皆能对应唯一一项输出值集合中的元素。例如实数x对应到其平方x的关系就是一个函数，若以3作为此函数的输入值，所得的输出值便是9。为方便起见，一般做法是以符号等等来指代一个函数。若函数以作为输入值，则其输出值一般写作，在英文中读作「f of x」，在中文中常读作「f x」。上述的平方函数关系写成数学式记为。函数的概念并不局限于数之间的映射关系，例如若定义函数为每个国家当前的首都，那么给予输入值西班牙就会输出唯一值马德里：。气温的分布也能用函数表达，以时间和地点作为参量输入，以该时该地的温度作为输出。表达函数有多种方式，例如解析法是用数学式表达两个变量之间的对应关系，图像法是用坐标系上的函数图形表达两个变量之间的对应关系，列表法用表格表达两个变量之间的对应关系。

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. Likewise, if the input is 3, then the output is also 9, and we may write f(3) = 9. (The same output may be produced by more than one input, but each input gives only one output.) The input variable(s) are sometimes referred to as the argument(s) of the function.