Consider the relation given by the graph as shown. 2 2 4 4 –2 –4 –2 –4 x y To find the domain, observe that • the leftmost point of the graph is (-3, 0). • the rightmost point of the graph is (3, 0). Since the graph continues without stopping between these values, the points on the graph have x-values between, and including, -3 and 3, as illustrated by Figure 3.2. So, the domain is the interval -3, 3. To find the range, observe that • the lowest point of the graph is (0, -2). • the highest point of the graph is (0, 2). Since the graph continues without stopping between these values, the points on the graph have y-values between, and including, -2 and 2, as illustrated by Figure 3.3. So, the range is the interval -2, 2. 4 0 (0 2) Recall that brackets are used to denote that a number is included in a set and parentheses are used to denote that a number is not included in a set. Brackets are used with the endpoints -3 and 3 since points with these x-values are included on the graph. Brackets are also used on -2 and 2 since points with these y-values are included on the graph. We will examine one more relation. In this case, the graph continues indefinitely in both directions. 6 2 –4 –2 2 x 4 4 6 –2 y (0 2) (3 0) (0 –2) (–3 0) 2 2 4 4 –2 –4 –2 –4 x y 2 –2 –4 y Figure 3.3 (3 0) (0 –2) (–3 0) 2 2 4 4 –2 –4 –2 –4 x y –4 –2 0 2 4 x Figure 3.2 168 Chapter 3 Graphs, Relations, and Functions
hendricks_intermediate_algebra_1e_ch1_3
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