Section 3.2 Relations 171 3e. Find the output value that corresponds to an input value of 0 for the relation given by the table. x 3 0 -1 0 3 y -2 -1 0 1 2 Solutions 3a. The input value is the x-value. The ordered pair in the relation with an x-value of 3 is (3, 9). Therefore, the output value that corresponds to x = 3 is y = 9. 3b. y2 = x Given relation (4)2 = x Replace the output value, y, with 4. 16 = x Simplify the exponent. The input value that corresponds to y = 4 is x = 16. 3c. y = |x - 4| Given relation y = |0 - 4| Replace the input value, x, with 0. y = |-4| Simplify. y = 4 Simplify the absolute value. The output value that corresponds to x = 0 is y = 4. 3d. The input value is 1, so x = 1. We need to find the point on the graph which has an x-value of 1. Since (1, -3) lies on the graph, the output value that corresponds to x = 1 is y = -3. 3e. The input value is x = 0. The ordered pairs in the given table with an x-value of 0 are (0, -1) and (0, 1). So, the output values that correspond to x = 0 are y = -1 and y = 1. Student Check 3 Find the indicated value for each relation. a. Find the output value that corresponds to the input value of 1 for the relation {(0, 3), (1, 5), (2, 7), (3, 9)}. b. Find the input value that corresponds to an output value of 5 for the relation y = 4x + 1. c. Find the output value that corresponds to an input value of -2 for the relation y = |x - 4|. d. Find the output value that corresponds to an input value of 0 for the relation given by the graph in Figure 3.7. e. Find the output value that corresponds to an input value of -3 for the relation given by the table. Troubleshooting Common Errors A common error associated with relations is shown. Objective 4 Example A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. Determine the domain and range of the relation represented by the graph. 6 2 –6 –4 –2 x 2 4 –2 y 2 2 4 4 –2 –4 –2 –4 x y (1 –3) x y -4 3 -3 4 -4 -3 -3 -4 -5 0 5 0 2 2 4 4 –2 –4 –2 –4 x y Figure 3.7 Objective 4 ▶ Troubleshoot common errors.
hendricks_intermediate_algebra_1e_ch1_3
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