Stitz-Zeager_College_Algebra_e-book

3 m1 x f x 3 2 x 3 2 will shift the graph of f

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Unformatted text preview: 4 4 (2, 3) 5, 3 3 (4, 3) (0, 1) 0, 1 2 3 y = f (x) 4 5 x vertical scaling by a factor of 1 2 1 2 4, 1 1 −− − − − − − − − −→ −−−−−−−−−− multiply each y -coordinate by 1 2 3 2 2, 2 2 y= 5 2 2 3 4 3 2 5 x 1 f (x) 2 These results are generalized in the following theorem. Theorem 1.5. Vertical Scalings. Suppose f is a function and a > 0. To graph y = af (x), multiply all of the y -coordinates of the points on the graph of f by a. We say the graph of f has been vertically scaled by a factor of a. • If a > 1, we say the graph of f has undergone a vertical stretch (expansion, dilation) by a factor of a. • If 0 < a < 1, we say the graph of f has undergone a vertical shrink (compression, contraction) 1 by a factor of a . A few remarks about Theorem 1.5 are in order. First, a note about the verbiage. To the authors, the words ‘stretch’, ‘expansion’, and ‘dilation’ all indicate something getting bigger. Hence, ‘stretched 8 Also called ‘vertical shrink,...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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