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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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