Example 1: The Square Function

The square function is defined by the rule

f(x) = x²

for each number x. The value of f(a) is found by squaring a. For instance, the values of f(0), f(2), f(-3), f(r), f(r+1) are

f(0) = 0, f(2) = 4, f(-3) = 9, f(r) = r², f(r + 1) = r² + 2r + 1.

The graph of the square function is the parabola with the equation y = x². The graph of y = x², with several points marked in, is shown in Figure 1.2.3.