Section 2.6 Functions-Transformations

Example 1 2 3 graph y x 2 1 graph y 5 x 2 graph

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Unformatted text preview: Graph y = −x 2 . 1 Graph y = 5 − . x +2 √ Graph y = 1 − x + 7. Outline Basic Functions Translations Reflections Scaling General Transformations Scaling Suppose y = f (x ) is function and c > 0 is a constant. If c > 1, then the graph of y = cf (x ) is the graph of y = f (x ) stretched vertically by a factor of c . If c < 1, then the graph of y = cf (x ) is the graph of y = f (x ) compressed vertically by a factor of c . If c > 1, then the graph of y = f (cx ) is the graph of 1 y = f (x ) compressed horizontally by a factor of c . If c < 1, then the graph of y = f (cx ) is the graph of 1 y = f (x ) stretched horizontally by a factor of c . Outline Basic Functions Examples Example 3 1 Graph y = |x |. 3 2 Graph y = . x √ Graph y = 2x . 4 Graph e x /4 . 1 2 Translations Reflections Scaling General Transformations Outline Basic Functions Translations Reflections Scaling General Transformations General Transformations If f is a function and a, b , h, and k are real numbers, then g (x ) = af (b (x − h)) + k is the graph of f : Translated vertically k units. Translated horizontally h units. Reflected across the x -axis if a < 0. Scaled vertically by a factor of |a|. Reflected across the y -axis if b < 0. 1 Scaled horizontally by a factor of |b| . Outline Basic Functions Translations Reflections Scaling General Transformations Multiple Transformations When doing multiple transformations, proceed in the order of operation. In particular, scaling and reflecting take precedence over shifts. Example 1 2 3 √ Graph y = 3 x + 1. 2 Graph y = . 1−x Graph y = (2 − 6x )1/3 ....
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