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29_Cal_Solution of Calculus_6e

# 29_Cal_Solution of Calculus_6e - Section 1.4 C01S04.001...

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Section 1.4 C01S04.001: Because g ( x ) = 2 x increases—first slowly, then rapidly—on the set of all real numbers, with values in the range (0 , + ), the given function f ( x ) = 2 x 1 must increase in the same way, but with values in the range ( 1 , + ). Therefore its graph is the one shown in Fig. 1.4.29. C01S04.002: Given: f ( x ) = 2 3 x . The graph of g ( x ) = 3 x increases, first slowly, then rapidly, on its domain the set R of all real numbers. Hence h ( x ) = 3 x decreases, first rapidly, then slowly, on R , with values in the interval (0 , + ). Hence j ( x ) = 3 x increases, first rapidly, then slowly, on R , with values in the interval ( −∞ , 0). Therefore f ( x ) = 2 3 x increases, first rapidly, then slowly, on R , with values in the interval ( −∞ , 2). Therefore its graph must be the one shown in Fig. 1.4.33. C01S04.003: The graph of f ( x ) = 1 + cos x is simply the graph of the ordinary cosine function raised 1 unit—moved upward 1 unit in the positive y -direction. Hence its graph is the one shown in Fig. 1.4.27.
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