As we have seen in examples above, we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.
The most common graphs name the input value x and the output value y, and we say y is a function of x, or y=f(x) when the function is named f. The graph of the function is the set of all points (x,y) in the plane that satisfies the equation y=f(x). If the function is defined for only a few input values, then the graph of the function is only a few points, where the x-coordinate of each point is an input value and the y-coordinate of each point is the corresponding output value. For example, the black dots on the graph in the graph below tell us that f(0)=2 and f(6)=1. However, the set of all points (x,y) satisfying y=f(x) is a curve. The curve shown includes (0,2) and (6,1) because the curve passes through those points.
Step-by-step explanation:
