Unformatted text preview: certainly build a table of values and connect the points, or we could take a step back and
x
1x
note that g (x) = 2 = 2−1 = 2−x = f (−x), where f (x) = 2x . Thinking back to Section 1.8,
2 Recall that this means there are no holes or other kinds of breaks in the graph.
You can actually prove this by considering the polynomial p(x) = x2 − 3 and showing it has no rational zeros by
applying Theorem 3.9.
4
This is where Calculus and continuity come into play.
5
Want more information? Look up “convergent sequences” on the Internet.
6
Meaning, graph some more examples on your own.
3 6.1 Introduction to Exponential and Logarithmic Functions 331 the graph of f (−x) is obtained from the graph of f (x) by reﬂecting it across the y axis. As such,
we have
y y
8
7 7 6 6 5 5 4 4 3 3 2 2 1
−3 −2 −1 8 1
1 2 3 reﬂect across y axis x y = f (x) = 2x −3 −2 −1 −− − − − −→
−−−−−− multiply each xcoordinate by −1 1 2 3 y = g (x) = 2−x = x 1x
2 We see that the domain and range of g match that of f , namely (−∞, ∞) and (0, ∞), respectively.
Like f , g is also onetoone. Whereas f is always increasing, g is always decreasing. As a result,
as x → −∞, g (x) → ∞, and on the ﬂip side, as x → ∞, g (x) → 0+ . It shouldn’t be too surprising
that for all choices of the base 0 <...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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