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Stitz-Zeager_College_Algebra_e-book

# This had the undesirable consequence of making the

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Unformatted text preview: 4 −2 −1 x 5 1 2 3 4 (−1, −1) 5 x (5, −1) −2 −2 (5, −2) shift up 1 unit y = m3 (x) = −m2 (x) = − 1 x 2 + 3 2 −− − − − −→ −−−−−− add 1 to each y -coordinate y = m(x) = m3 (x) + 1 = − 1 x 2 + 3 2 +1 Some comments about Example 1.8.3 are in order. First, recalling the properties of radicals from Intermediate Algebra, we know that the functions g and j are the same, since j and g have the √ √√ √ same domains and j (x) = 9x = 9 x = 3 x = g (x). (We invite the reader to verify that the all of the points we plotted on the graph of g lie on the graph of j and vice-versa.) Hence, for √ f (x) = x, a vertical stretch by a factor of 3 and a horizontal shrink by a factor of 9 result in the same transformation. While this kind of phenomenon is not universal, it happens commonly enough with some of the families of functions studied in College Algebra that it is worthy of note. Secondly, to graph the function m, we applied a series of four transformations. While it would have been easier on the authors to simply inform the reader of which steps to ta...
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