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chapter 1 1 - 1 El FUNCTIONSAND MODELS 1.1 Four Ways to...

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Unformatted text preview: 1 El FUNCTIONSAND MODELS 1.1 Four Ways to Represent a Function In exercises requiring estimations or approximations, your answers may vary slightly from the answers given here. 1. (a) The point (‘1, —2) is on the graph off, so f(—1)= —2. (b) When a: = 2, y is about 2.8, so f(2) m 2.8. (c) f(:c) = 2 is equivalent to y = 2. When y : 2, we have x = 73 and :c = 1. (d) Reasonable estimates for a: when 3/ = O are m = —2.5 and a: : 0.3. (e) The domain of f consists of all az-values on the graph of f. For this function, the domain is —3 S a: g 3, or [—3, 3]. The range of f consists of all y—values on the graph of f. For this function, the range is —2 g y g 3, or [—2, 3]. (f) As at increases from —1 to 3, y increases from —2 to 3. Thus, f is increasing on the interval {—1, 3]. 2. (a) The point (—4, ~2) is on the graph of f, so f(—4) = —2. The point (3, 4) is on the graph of g, so 9(3) 2 4. (b) We are looking for the values of as for which the y-values are equal. The y—values for f and g are equal at the points (—2, 1) and (2,2), so the desired values ofa: are —2 and 2. (c) f(:::) = —1 is equivalent to y = —1. When 3; = —1, we have m : —3 and a: = 4. ((1) As m increases from 0 to 4, y decreases from 3 to —-1. Thus, f is decreasing on the interval [0,4]. (e) The domain of f consists of all m-values on the graph off. For this function, the domain is —4 S m S 4, or {—4, 4]. The range of f consists of all y-values on the graph of f. For this function, the range is —2 S y g 3, or [~2, 3]. (f) The domain ofg is [~4, 3] and the range is [0.5, 4]. 3. From Figure 1 in the text, the lowest point occurs at about (t, a) = (12, —85). The highest point occurs at about (17, 115). Thus, the range of the vertical ground acceleration is —85 S a S 115. In Figure 11, the range of the north—south acceleration is approximately —325 S a g 485. In Figure 12, the range of the east—west acceleration is approximately —210 S a S 200. 4. Example 1: A car is driven at 60 mi / h for 2 hours. The distance d miles traveled by the car is a function of the time t. The domain of the 120 function is {t | 0 S t g 2}, where t is measured in hours. The range of the function is {d | 0 S d S 120}, where dis measured in miles. 0 2 time in hours ...
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