Unformatted text preview: from, the output of
a function causes the graph to shift up or down, respectively”. So what happens if we add to or
subtract from the input of the function?
Keeping with the graph of y = f (x) above, suppose we wanted to graph g (x) = f (x + 2). In other
words, we are looking to see what happens when we add 2 to the input of the function.1 Let’s try
to generate a table of values of g based on those we know for f . We quickly ﬁnd that we run into
some diﬃculties.
1 We have spent a lot of time in this text showing you that f (x + 2) and f (x) + 2 are, in general, wildly diﬀerent
algebraic animals. We will see momentarily that the geometry is also dramatically diﬀerent. 86 Relations and Functions x
0
2
4
5 (x, f (x)) f (x)
g (x) = f (x + 2)
(x, g (x))
(0, 1)
1
f (0 + 2) = f (2) = 3
(0, 3)
(2, 3)
3
f (2 + 2) = f (4) = 3
(2, 3)
(4, 3)
3
f (4 + 2) = f (6) =?
(5, 5)
5
f (5 + 2) = f (7) =? When we substitute x = 4 into the formula g (x) = f (x + 2), we are asked to ﬁnd f (4 + 2) = f (6)
which doesn’t exist bec...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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