Stitz-Zeager_College_Algebra_e-book

# 8 transformations 105 3 the complete graph of y f x is

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Unformatted text preview: ke, we have strived to explain why the order in which the transformations were applied made sense. We generalize the procedure in the theorem below. Theorem 1.7. Transformations. Suppose f is a function. To graph g (x) = Af (Bx + H ) + K 1. Subtract H from each of the x-coordinates of the points on the graph of f . This results in a horizontal shift to the left if H > 0 or right if H < 0. 2. Divide the x-coordinates of the points on the graph obtained in Step 1 by B . This results in a horizontal scaling, but may also include a reﬂection about the y -axis if B < 0. 3. Multiply the y -coordinates of the points on the graph obtained in Step 2 by A. This results in a vertical scaling, but may also include a reﬂection about the x-axis if A < 0. 4. Add K to each of the y -coordinates of the points on the graph obtained in Step 3. This results in a vertical shift up if K > 0 or down if K < 0. Theorem 1.7 can be established by generalizing the techniques developed in this section. Suppose (a, b) is on the graph of f . Then f (a) = b,...
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