Example on how to do exercise 2: Graphing a constant function Graph f(x) = 3, and state the domain and range. Solution The graph of f(x) = 3 is the same as the graph of y = 3, which is the horizontal line in Fig XXXXXXXXXXSince any real number can be used for x in f(x) = 3 and since the line in Fig. 11.5 extends without bounds to the left and right, the domain is the set of all real numbers, (-8, 8). Since the only y-coordinate for f(x) = 3 is 3, the range is {3}. Figure 11.5 Now do Exercises 1–2 The domain and range of a function can be determined from the formula or the graph. However, the graph is usually very helpful for understanding domain and range. Exercise 2 f(x) = 4 Graph this function, and state its domain and range. See Example above. Example on how to do exercise 56: Graphing relations that are not functions Graph each relation, and state the domain and range. a)x = y2b)x = | y - 3 |Solution a)Because the equation x = y2 expresses x in terms of y, it is easier to choose the y-coordinate first and then find the x-coordinate: Figure 11.16 shows the graph. The domain is [0, 8) and the range is (-8, 8). Figure 11.16b)Again we select values for y first and find the corresponding x-coordinates: Plot these points as shown in Fig XXXXXXXXXXThe domain is [0, 8) and the range is (-8, 8). Figure 11.17 Now do Exercises 45–56 Exercise 56 x = (y + 2)2 Graph each relation, and state its domain and range. See Example above.
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