Unformatted text preview: 6 −5 −4 −3 −2 −1 1 2 3 4 5 6 x −2
−3
−4
−5 .
.
. −6 The graph of f (x) = x .
(b) Note that f (1.1) = 1, but f (−1.1) = −2, and so f is neither even nor odd. 84 1.8 Relations and Functions Transformations In this section, we study how the graphs of functions change, or transform, when certain specialized
modiﬁcations are made to their formulas. The transformations we will study fall into three broad
categories: shifts, reﬂections, and scalings, and we will present them in that order. Suppose the
graph below is the complete graph of f .
y
(5, 5)
5
4 (2, 3)
3 (4, 3)
2 (0, 1)
1 2 3 4 5 x y = f (x) The Fundamental Graphing Principle for Functions says that for a point (a, b) to be on the graph,
f (a) = b. In particular, we know f (0) = 1, f (2) = 3, f (4) = 3 and f (5) = 5. Suppose we wanted to
graph the function deﬁned by the formula g (x) = f (x) + 2. Let’s take a minute to remind ourselves
of what g is doing. We start with an input x to the function f and we obtain the output f (x).
The f...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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