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**Unformatted text preview: **unction g takes the output f (x) and adds 2 to it. In order to graph g , we need to graph the
points (x, g (x)). How are we to ﬁnd the values for g (x) without a formula for f (x)? The answer is
that we don’t need a formula for f (x), we just need the values of f (x). The values of f (x) are the
y values on the graph of y = f (x). For example, using the points indicated on the graph of f , we
can make the following table.
x
0
2
4
5 (x, f (x)) f (x) g (x) = f (x) + 2 (x, g (x))
(0, 1)
1
3
(0, 3)
(2, 3)
3
5
(2, 5)
(4, 3)
3
5
(4, 5)
(5, 5)
5
7
(5, 7) In general, if (a, b) is on the graph of y = f (x), then f (a) = b, so g (a) = f (a) + 2 = b + 2. Hence,
(a, b +2) is on the graph of g . In other words, to obtain the graph of g , we add 2 to the y -coordinate
of each point on the graph of f . Geometrically, adding 2 to the y -coordinate of a point moves the
point 2 units above its previous location. Adding 2 to every y -coordinate on a graph en masse is
usually described as ‘shifting the graph u...

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