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Unformatted text preview: Chapter 5 Outline Math 110 If a >0, then f(x-a) is f(x) shifted to the right, and f(x+a) is f(x) shifted to the left (by a). If c is any real number, then f(x) + c is a vertical shift by c. Horizontal and vertical shifts commute. If B is greater than one, then f(Bx) is a horizontal contraction of f(x). Sometimes it is helpful to think this way: If f(1) = 0, and B = 2, and you plug in x = 1/2, then f(2/2) = f(1)=0, so the location of the zero has gotten squished closer to the y-axis. If B is between 0 and 1, then f(Bx) is a horizontal expansion of f(x). In the above example, if B = , and you plug in x = 2, then f(2/2) = f(1) = 0, so the location of the zero has gotten further away from the y-axis. Horizontal stretches commute with vertical shifts. But not with horizontal shifts. Indeed, f(2(x-1)) is a horizontal contraction by 2, followed by a horizontal shift to the right by 1, whereas f(2x-1) is a horizontal shift to the right by 1 followed by a horizontal contraction...
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- Fall '08