3-5 Transformations - 3-5 Transformations...

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3-5: Transformations Vertical Shifts:   If a real number c is added to the function y = f(x), the graph of the new function y =  f(x) + c is the graph of f shifted up if c > 1, down if c < 1. Horizontal Shifts:   If x in a function y = f(x) is replaced by x – c (c a real number), the graph of the  new function y = f(x - c) is shifted horizontally left if c < 0) or right if c > 0.  Stretches and compressions:  When a function y = f(x) is multiplied by a positive number k, the  graph of the new function y = kf(x) is vertically compressed if 0 < k < 1 or stretched if k > 1. Reflection about the x-axis:   When the function y = f(x) is multiplied by –1, the graph of the new  function y = -f(x) is the reflection about the axis. Graph: (1) a. y = f(x) = | x | c. y = f(x) = | x - 2 | (2) a. y = f(x) = x 2 b. y = f(x) = | x | - 3 d. y = f(x) = | x - 2 | - 3 b.
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