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M1410107

# M1410107 - (Section 1.7 Transformations 1.83 SECTION 1.7...

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(Section 1.7: Transformations) 1.83 SECTION 1.7: TRANSFORMATIONS PART A: TRANSLATIONS Translations are transformations that move a graph without changing its shape or orientation. Let G be the graph of y = f x ( ) . Let c be a positive real number c R + ( ) . Vertical Shifts The graph of y = f x ( ) +c is G shifted up by c units. The graph of y = f x ( ) - c is G shifted down by c units. Horizontal Shifts The graph of y = f x c ( ) is G shifted right by c units. The graph of y = f x +c ( ) is G shifted left by c units. Warning: Many people confuse the Horizontal Shifts. You may want to think, “It’s the opposite from what you expect.” Another approach: If 0 is in the domain of f , then the y -coordinate at x = 0 for the graph of y = f x ( ) becomes the y -coordinate at x = c for the graph of y = f x c ( ) . Both arguments for f are 0 in those cases. Informally, what “happened” at x = 0 now “happens” at x = c . PART B: REFLECTIONS (“MIRROR IMAGES”) The graph of y = f x ( ) is G reflected about the x -axis. The graph of y = f x ( ) is G reflected about the y -axis. If reflecting a graph about an axis yields the same graph, then that graph is symmetric about that axis; see Notes 1.51 . Reflections, like translations, are actions performed on a graph, while symmetries are properties inherent to a graph.

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1.84 PART C: EXAMPLES Example Let f x ( ) = x . Translations:
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M1410107 - (Section 1.7 Transformations 1.83 SECTION 1.7...

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