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Stitz-Zeager_College_Algebra_e-book

# 83 are in order first recalling the properties of

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Unformatted text preview: other words, we are looking to see what eﬀect multiplying the inputs to f by 2 has on its graph. If we attempt to build a table directly, we quickly run into the same problem we had in our discussion leading up to Theorem 1.3, as seen in the table on the left below. We solve this problem in the same way we solved this problem before. For example, if we want to determine the point on g which corresponds to the point (2, 3) on the graph of f , we set 2x = 2 so that x = 1. Substituting x = 1 into g (x), we obtain g (1) = f (2 · 1) = f (2) = 3, so that (1, 3) is on the graph of g . Continuing in this fashion, we obtain the table on the lower right. x 0 2 4 5 (x, f (x)) f (x) g (x) = f (2x) (x, g (x)) (0, 1) 1 f (2 · 0) = f (0) = 1 (0, 1) (2, 3) 3 f (2 · 2) = f (4) = 3 (2, 3) (4, 3) 3 f (2 · 4) = f (8) =? (5, 5) 5 f (2 · 5) = f (10) =? x 0 1 2 2x g (x) = f (2x) (x, g (x)) 0 g (0) = f (0) = 1 (0, 0) 2 g (1) = f (2) = 3 (1, 3) 4 g (2) = f (4) = 3 (2, 3) 5 5 5 g 2 = f (5) = 5 2, 5 5 2 In general, if (a, b)...
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