Stitz-Zeager_College_Algebra_e-book

Suppose we wish to graph the function g x 2f x where f

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Unformatted text preview: aph y = −f (x) by reflecting the graph of f about the x-axis 4 The expressions −f (x) and f (−x) should look familiar - they are the quantities we used in Section 1.7 to test if a function was even, odd, or neither. The interested reader is invited to explore the role of reflections and symmetry of functions. What happens if you reflect an even function across the y -axis? What happens if you reflect an odd function across the y -axis? What about the x-axis? 90 Relations and Functions y y (5, 5) 5 5 4 4 (2, 3) 3 3 (4, 3) 2 2 (0, 1) 1 1 2 3 4 x 5 1 −1 −2 3 4 5 x −2 −3 2 (0, −1) −3 (4, −3) (2, −3) −4 −4 −5 −5 (5, −5) reflect across x-axis −− − − − −→ −−−−−− multiply each y -coordinate by −1 y = f ( x) y = −f (x) By reflecting the graph of f across the y -axis, we obtain the graph of y = f (−x). y y (−5, 5) (5, 5) 5 5 4 (−2, 3) (2, 3) 3 3 (−4, 3) (4, 3) 2 2 (0, 1) −5 −4 −3 −2 −1 4 (0, 1) 1 2 3 4 5 x reflect across y -axis −− − − − −→ −−−−−− y = f (x) multiply each x-coordinate by −1 −5 −4 −3 −2 −1 1 2 3 4 5 x y = f (−x) With the addition of reflections, it is now more important than ever to consider the order of transformations, as the next example illustrates. √ Example 1.8...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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