Lec 05 Fig 2: Graphical illustration of a function

We can illustrate (or even define) a function by a graph. Conventionally, we use the horizontal axis to represent the input and the vertical axis to represent the output. For example, \(f(0) = 4\) can be represented by a point \((0,4)\). If we generate all the input/output pairs of a function and plot them on a graph, we get a graphical representation of the function. The following graph illustrates how the function \(f(x) = \sqrt{16-x^2}\) behaves. This function represents the top half of the circle of radius 4 centred at \((0,0)\).