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| Introduction to Transformation
Given: f(x) g(x) = A f(B(x)-h) + D g(x) = +/-A f(+/-B(x)-h)+D h = horizontal shift: +h is shift to right; -h (x+h) is shift to left B = horizontal stretch: 0<B<1 is stretch; B>1 is compression -B = reflection about the y-axis A = vertical stretch: A>1 is stretch; A < 1 is compression -A = refection about x-axis D = vertical shift: +D is shift up ; -D is shift
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| Order of Transformation
Given: f(x) g(x) = +/-A f(+/-B(x)-h)+D 1. h = horizontal shift 2. B = horizontal stretch / compression 3. -B = reflection about the y-axis 4. A = vertical stretch / compression 5. -A = refection about x-axis 6. D = vertical shift
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1. Horizontal shift y = f(x-h)
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2. Horizontal stretch / compression y = fB(x)
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3. Horizontal reflection about y-axis: y=f(-x)
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4. Vertical Stretch / Compression: y = A f(x)
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5 Vertical Reflection about x-axis (-A): y = - A f(x)
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5. Vertical reflection example 2
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6.vertical shift: y = f(x) + D
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Example 2
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Example 3
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