In mathematics, when one quantity depends on a second quantity, the first is said to be a function of the second. The calculation of the area of a circle, for example, depends on the radius. So, the area of a circle is a function of the radius. Consider the following equation:
y = 3x − 5
This equation can be considered a function in which x is the independent variable and y is the dependent variable. In terms of a function, x is the domain of the function, and can be any number. The entire scope of numbers x can assume is called the range, such as 1, 2, 3, and so on. y is said to be the value of the function. This makes sense because, for whatever number x can be, there will also be a corresponding value for y.
In mathematics there is a notation reserved for representing functions. Consider the following two functions:
y = 5x + 3 | y = 9x − 7 |
These are two separate functions, and each can be given a name. Since f is often used to denote a function, we'll call the first one f and the second one g.
Here are the two functions f and g again. The parentheses are used after the name of the function and inside the parentheses are the arguments of the function.
f(x) = 5x + 3 | g(x) = 9x − 7 |
These functions have one argument each, namely x. So, each function expects a value for x as its input. Consider the following:
f(x) = 5x + 3
Where x = 3:
f(3) = 15 + 3 = 18
Since functions evaluate to a single value, functions can also be used as arguments to other functions. This is demonstrated in the following example. g is evaluated first and its value is passed on to f as an argument.
f(g(x))