Stitz-Zeager_College_Algebra_e-book

# G x 2 3 x 3 1 or g x 2 3 x 3 1 1 2x y 1 2 x 2

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Unformatted text preview: f and g side-by-side gives −3, 2 y 13 2 6 6 5 5 4 4 (0, 3) 3 3 −1,2 2 2 (−2, 0) 1 −4 −3 −2 −1 −1 −3 −4 3 ,2 2 (2, 0) 1 2 3 4 x −2 (−4, −3) 5 13 , 22 y −4 −3 −2 −1 −1 1 2 −2 (4, −3) −3 −4 1 ,−5 2 2 3 4 x 102 Relations and Functions The reader is strongly encouraged11 to graph the series of functions which shows the gradual transformation of the graph of f into the graph of g . We have outlined the sequence of transformations in the above exposition; all that remains is to plot all ﬁve intermediate stages. Our last example turns the tables and asks for the formula of a function given a desired sequence of transformations. If nothing else, it is a good review of function notation. Example 1.8.5. Let f (x) = x2 . Find and simplify the formula of the function g (x) whose graph is the result of f undergoing the following sequence of transformations. Check your answer using a graphing calculator. 1. Vertical shift up 2 units 2. Reﬂection across the x-axis 3. Horizontal shift right 1 unit 4. Horizontal stretch by a factor o...
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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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