6.4 Visual presentation

Just as functions of one variable (one input) can be represented graphically, so can functions of 2 variables. However, we now need a 3 dimensional picture. This graphic shows the relationship between the weight of a car, the horsepower of its engine, and its fuel economy. Here, the fuel economy is the dependent variable, and weight and horsepower are described as the independent variables.

A plane is drawn through the points (spheres), that captures to some extent the from of the relationship. A plane is the extension to 3-dimensions of the 2 dimensional concept of a straight line. We will continue this topic in the next class. More complicated relationships may in fact depend on many independent variables, there is no reason why we have to stop at 2. For example, a function of 3 variables is represented as z = f(s,t,u), indicating that there are 3 inputs.