Stitz-Zeager_College_Algebra_e-book

Plotting f and g side by side gives 3 2 y 13 2 6 6 5

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Unformatted text preview: 2, we solve 2 x + 3 = 4. Our first step is to subtract the 3 (the horizontal 2 2 1 5 shift) to obtain 2 x = 2 . Next, we multiply by 2 (the horizontal stretch) and obtain x = 5. We define two intermediate functions to handle first the shift, then the stretch. In accordance with Theorem 1.3, m1 (x) = f x + 3 2 = x+ 3 2 will shift the graph of f to the left 3 2 units. 98 Relations and Functions y y (4, 2) 5 ,2 2 2 2 (1, 1) −1,1 2 1 (0, 0) −3 −2 −1 1 2 3 4 5 −3 −2 −1 −3,0 2 x −1 1 2 3 3 2 = 4 x+ x 5 3 2 −2 −2 3 shift left 2 units y = f (x) = √ −− − − − −→ −−−−−− subtract 3 from each x-coordinate 2 x 1 Next, m2 (x) = m1 2 x = 1 x + 2 graph of m1 by a factor of 2. y 3 2 y = m1 (x) = f x + will, according to Theorem 1.6, horizontally stretch the y 5 ,2 2 2 (5, 2) 2 (−1, 1) 1 −2,1 −3 −2 −1 −3,0 2 1 2 3 4 5 −2 −1 x (−3, 0) 1 2 3 4 x 5 −1 −2 −2 horizontal scale by a factor of 2 y = m1 (x) = x+ −− − − − − − − −→ −...
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