Section 2.6 Functions-Transformations

# Horizontal and vertical translations and reections

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Unformatted text preview: and reﬂections are rigid transformations. A nonrigid transformation of a graph changes its shape. A scaling is a nonrigid transformation. Outline Basic Functions Translations Reﬂections Scaling General Transformations Translations Suppose y = f (x ) is function and c > 0 is a constant. The graph of y = f (x ) + c is the graph of y = f (x ) shifted up c units. The graph of y = f (x ) − c is the graph of y = f (x ) shifted down c units. The graph of y = f (x − c ) is the graph of y = f (x ) shifted right c units. The graph of y = f (x + c ) is the graph of y = f (x ) shifted left c units. Example 3 4 Graph y = (x − 2)2 − 5. 2 Graph y = √ x + 1. 1 Graph y = . x −4 Graph y = |x | + 3. 1 Outline Basic Functions Translations Reﬂections Scaling General Transformations Reﬂections Suppose y = f (x ) is function. The graph of y = −f (x ) is the graph of y = f (x ) reﬂected across the x -axis. The graph of y = f (−x ) is the graph of y = f (x ) reﬂected across the y -axis. Example 1 2 3...
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