A function is a relationship between inputs and outputs with a specific property that one input is related to only one output. The input of a function is usually denoted as x, while the output of x is denoted as f(x), which stands for ‘function of x.’ The input and output of a function can be described as an ordered pair. For example, consider the following function:
F(x) = x^2 + 3x + 2
If the input x was 1, then the output would be
F(x) = (1)^2+3(1)+2 = 1+3+2 = 6
Thus, the ordered pair can be written as (1,6)
If the input x was 2, then the output would be 12, and the ordered pair would be (2,12)
In mathematics, the graph of a function is just an illustration of all the ordered pairs. So for the above equation, (1,6) and (2,12) as calculated previously would be plotted. Other ordered pairs for the inputs 3, 4 and 5 are calculated below:
With these ordered pairs, a simple plot can be graphed to show the general relationship between the input and output of a particular function. Thus, understanding the rules and properties of functions, as well as how to graph them, is particularly important in the discipline of Algebra.