Stitz-Zeager_College_Algebra_e-book

Y y 1 2 2 2 2 1 2 1 1 2 1 3 0 3 0 4

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Unformatted text preview: shall see in the next example that order is generally important when applying more than one transformation to a graph. 3 We could equally have chosen the convention ‘outputs first’. 1.8 Transformations 89 Since m(x) = f (x + 3) − 2 and f (x + 3) = m1 (x), we have m(x) = m1 (x) − 2. We can apply Theorem 1.2 and obtain the graph of m by subtracting 2 from the y -coordinates of each of the points on the graph of m1 (x). The graph verifies that the domain of m is [−3, ∞) and we find the range of m is [−2, ∞). y y (1, 2) 2 2 1 (−2, 1) 1 (1, 0) (−3, 0) −3 −2 −1 −1 1 2 3 4 x −3 −2 −1 −1 (−2, −1) 2 3 4 x −2 −2 shift down 2 units y = m1 (x) = f (x + 3) = 1 √ −− − − − −→ −−−−−− x+3 subtract 2 from each y -coordinate (−3, −2) y = m(x) = m1 (x) − 2 = √ x+3−2 Keep in mind that we can check our answer to any of these kinds of problems by showing that any of the points we’ve moved lie on the graph of our final answer. For example, we can check that...
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