Stitz-Zeager_College_Algebra_e-book

# 18 transformations 95 by a factor of 2 makes sense if

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Unformatted text preview: s the range of f , namely [0, ∞). y y (4, 2) 2 2 (−4, 2) (1, 1) 1 1 (−1, 1) (0, 0) −4 −3 −2 −1 1 y = f (x) = 2 √ 3 x 4 reﬂect across y -axis −− − − − −→ −−−−−− multiply each x-coordinate by −1 x (0, 0) −4 −3 −2 −1 1 2 y = g (x) = f (−x) = √ 3 4 x −x √ 2. To determine the domain of j (x) = 3 − x, we solve 3 − x ≥ 0 and get x ≤ 3, or (−∞, 3]. To determine which transformations we need to apply to the graph of f to obtain the graph √ √ of j , we rewrite j (x) = −x + 3 = f (−x + 3). Comparing this formula with f (x) = x, we see that not only are we multiplying the input x by −1, which results in a reﬂection across the y -axis, but also we are adding 3, which indicates a horizontal shift to the left. Does it matter in which order we do the transformations? If so, which order is the correct order? Let’s consider the point (4, 2) on the graph of f . We refer to the discussion leading up to Theorem 1.3. We know f (4) = 2...
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