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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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