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Stitz-Zeager_College_Algebra_e-book

# J x 9x 3 mx 1 x3 2 solution 1 first we note

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Unformatted text preview: (−(x + 3)) = f (−x − 3) = −x − 3 which isn’t what we want. However, if we did the reﬂection ﬁrst and followed it by a shift to the right 3 units, we would have arrived at the function j (x). We leave it to the reader to verify the details. 1.8 Transformations 93 y y 3 (0, 3) 2 2 1 1 (1, 2) (4, 1) 1 (0, 0) 2 3 x 4 1 −2 2 3 4 x −1 −1 (1, −1) shift up 3 units (4, −2) −− − − − −→ −−−−−− −2 add 3 to each y -coordinate √ y = m1 (x) = − x √ y = m(x) = m1 (x) + 3 = − x + 3 We now turn our attention to our last class of transformations, scalings. Suppose we wish to graph the function g (x) = 2f (x) where f (x) is the function whose graph is given at the beginning of the section. From its graph, we can build a table of values for g as before. y (5, 5) 5 4 (2, 3) 3 (4, 3) 2 (0, 1) 1 2 3 4 5 x x 0 2 4 5 (x, f (x)) f (x) g (x) = 2f (x) (x, g (x)) (0, 1) 1 2 (0, 2) (2, 3) 3 6 (2, 6) (4, 3) 3 6 (4, 6) (5, 5) 5 10 (5, 10) y = f (x) In general, if (a, b) is on...
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