Stitz-Zeager_College_Algebra_e-book

4 use your graph in 1 to graph mx x 3 2 1 graph f

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Unformatted text preview: p 2 units’. Notice that the graph retains the same basic shape as before, it is just 2 units above its original location. In other words, we connect the four points we moved in the same manner in which they were connected before. We have the results side-by-side below. 1.8 Transformations 85 y y (5, 7) 7 7 6 6 (5, 5) (2, 5) 5 5 (4, 5) 4 4 (2, 3) (0, 3) 3 (4, 3) 2 2 (0, 1) 1 1 2 3 4 5 x shift up 2 units 1 2 3 4 5 x −− − − − −→ −−−−−− y = f (x) add 2 to each y -coordinate y = g (x) = f (x) + 2 You’ll note that the domain of f and the domain of g are the same, namely [0, 5], but that the range of f is [1, 5] while the range of g is [3, 7]. In general, shifting a function vertically like this will leave the domain unchanged, but could very well affect the range. You can easily imagine what would happen if we wanted to graph the function j (x) = f (x) − 2. Instead of adding 2 to each of the y -coordinates on the graph of f , we’d be subtracting 2. Geometrically, we would be moving the graph down 2 units. We leave i...
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