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hendricks_intermediate_algebra_1e_ch1_3

170 Chapter 3 Graphs, Relations, and Functions Solutions 2a. There is no leftmost or rightmost point on the graph as indicated by the arrows. The graph extends indefinitely left to -∞ and right to ∞. So, the domain is all real numbers, or (-∞, ∞). There is no lowest or highest point on the graph as indicated by the arrows. The graph extends indefinitely downward to -∞ and upward to ∞. So, the range is all real numbers, or (-∞, ∞). 2b. There is no leftmost or rightmost point on the graph as indicated by the arrows. The graph extends indefinitely left to -∞ and right to ∞. So, the domain is all real numbers, or (-∞, ∞). The lowest point on the graph is (0, -4). There is no highest point on the graph as indicated by the arrows. The graph extends up to ∞. So, the range is -4, ∞). 4 2 2 –2 –2 –4 y –2 0 2 4 6 x 4 2 –2 –4 –2 –4 y –4 –2 0 2 4 x Student Check 2 Determine the domain and range of each relation from its graph. a. y = x - 3 b. y = |x + 1| 2 y 2 4 4 6 –2 –2 –4 –6 x 2 2 4 4 –2 –6 –4 –2 –4 x y 4 6 x 4 2 0 –2 –4 y 4 2 0 –2 –4 2 4 x y Determining Input and Output Values Knowing the relationship between two sets of information enables us to find unknown information. We often have to find an output value for a given input value or find an input value for a given output value. This task is performed nearly every day by each of us. How often have we had to find the tip on a meal, find the sales price of an item, or find directions to a specific location? In each of these cases, we know one value and must find another value that corresponds to it. Objective 3 Examples Find the indicated value for each relation. 3a. Find the output value that corresponds to the input value of 3 for the relation {(0, 3), (1, 5), (2, 7), (3, 9)} 3b. Find the input value that corresponds to an output value of 4 for the relation y2 = x. 3c. Find the output value that corresponds to an input value of 0 for the relation y = |x - 4|. 3d. Find the output value that corresponds to an input value of 1 for the relation given by the graph in Figure 3.6. 2 2 4 4 –2 –4 –2 –4 x y Figure 3.6 Objective 3 ▶ Determine input and output values for a relation.


hendricks_intermediate_algebra_1e_ch1_3
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