Stitz-Zeager_College_Algebra_e-book

Example 182 let f x x use the graph of f from example

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Unformatted text preview: in 1 to graph m(x) = x + 3 − 2. 1. Graph f (x) = Solution. 1. Owing to the square root, the domain of f is x ≥ 0, or [0, ∞). We choose perfect squares to build our table and graph below. From the graph we verify the domain of f is [0, ∞) and the range of f is also [0, ∞). y x 0 1 4 f (x) (x, f (x)) 0 (0, 0) 1 (1, 1) 2 (4, 2) (4, 2) 2 (1, 1) 1 (0, 0) 1 2 y = f (x) = 3 √ 4 x x 2. The domain of g is the same as the domain of f , since the only condition on both functions is that x ≥ 0. If we compare the formula for g (x) with f (x), we see that g (x) = f (x) − 1. In other words, we have subtracted 1 from the output of the function f . By Theorem 1.2, we know that in order to graph g , we shift the graph of f down one unit by subtracting 1 from each of the y -coordinates of the points on the graph of f . Applying this to the three points we have specified on the graph, we move (0, 0) to (0, −1), (1, 1) to (1, 0), and (4, 2) to (4, 1). The rest of the points follow suit, and we connect them with the same basic shape as before. We con...
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