Unformatted text preview: Chapter 5 Outline – Math 110 • If a >0, then f(xa) 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 yaxis. • If B is between 0 and 1, then f(Bx) is a horizontal expansion of f(x). In the above example, if B = ½, 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 yaxis. • Horizontal stretches commute with vertical shifts. But not with horizontal shifts. Indeed, f(2(x1)) is a horizontal contraction by 2, followed by a horizontal shift to the right by 1, whereas f(2x1) is a horizontal shift to the right by 1 followed by a horizontal contraction...
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 Fall '08
 BLAKELOCK
 Math, Addition, vertical shifts, A. Reflections

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