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Example 4: Functions Described by Explicitly Giving Its Domain
Let f be the function given by the rule f(t) = Thus f(x) is the positive square root of 1  x^{2}. The domain of f is the closed interval [1, 1]. The range of f is [0, 1]. For instance, f(2) is undefined, f(1) = 0, f(0) = 1, f(½) = . f(1) = 0, f(2) is undefined. The graph of f is given by the equation y = The equation can also be written in the form x^{2} + y^{2} = 1, y ≥ 0. The graph is just the upper half of the unit semicircle, shown in Figure 1.2.6. Figure 1.2.6 Sometimes a function is described by explicitly giving its domain in addition to a rule.


Home Real and Hyperreal Numbers Functions of Real Numbers Examples Functions Described by Explicitly Giving Its Domain 