232 CHAPTER 2 Graphs and Functions 2.3 Exercises CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. 1. The domain of the relation 513, 52, 14, 92, 110, 1326 is . 2. The range of the relation 513, 52, 14, 92, 110, 1326 is . 3. The equation y = 4x - 6 defines a function with independent variable and dependent variable . 4. The function y = 4x - 6 includes the ordered pair 16, 2. 5. For the function ƒ1x2 = -4x + 2, ƒ1-22 = . 6. For the function g1x2 = 2x, g192 = . 7. The function g1x2 = 2x has domain . 8. The function g1x2 = 2x has range . 9. The largest open interval over which the function graphed here increases is . 10. The largest open interval over which the function graphed here decreases is . 0 3 1 (3, 1) x y Determine whether each relation defines a function. See Example 1. 11. 515, 12, 13, 22, 14, 92, 17, 826 12. 518, 02, 15, 72, 19, 32, 13, 826 13. 512, 42, 10, 22, 12, 626 14. 519, -22, 1-3, 52, 19, 126 15. 51-3, 12, 14, 12, 1-2, 726 16. 51-12, 52, 1-10, 32, 18, 326 SOLUTION (a) The maximum height of the kite is 175 ft. This occurs at t = 5 min. The point 15, 1752 is the highest point on the graph, which occurs where the function changes from increasing to decreasing. (b) The minimum height of the kite between 5 and 15 min is 125 ft, which occurs at t = 10 min. The point 110, 1252 is a low point on the graph where the function changes from decreasing to increasing. We say that 125 ft is a relative minimum because it represents the lowest value on the graph for an interval of values near time t = 10 min. The absolute minimum value of 0 ft occurs at t = 0 min and t = 25 min, when the kite is on the ground. (c) The height of the kite is increasing from 0 to 5 min, and then again from 10 to 15 min. The height decreases from 5 to 10 min and from 20 to 25 min. The height is constant from 15 to 20 min. (d) The kite is on the ground initially and then rises rapidly to a height of 175 ft during the first 5 min. For the next 5 min, the height decreases. At 10 min, the height increases again, until it reaches a height of 150 ft after 15 min. For the next 5 min, the height remains the same, and then the kite falls back to the ground after 25 min. S Now Try Exercise 93. t y = h(t) 50 5 10 15 20 25 100 Minutes Height of a Kite Height (in feet) 0 150 200 Figure 30 (repeated)
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