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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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