Post on 14-Dec-2015
Copyright © 2000 by the McGraw-Hill Companies, Inc.
C H A P T E R 1
Functions, Graphs, and Limits
Copyright © 2000 by the McGraw-Hill Companies, Inc.
Figure 1.1 Interpretations of the function f(x).
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Figure 1.2 The composition f(g(x)) as an assembly line.
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Figure 1.3 (a) A production function. (b) Bounded population growth.
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Figure 1.4 (a) The graph of y = x2. (b) Other graphs through the points in Example 2.1.
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Figure 1.5 The graph of f(x) =
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Figure 1.6 The graph of f(x) = –x2 + x + 2.
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Figure 1.7 The graph of the functiony = x3 – x2 – 6x.
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Figure 1.8 The graph of the parabola y = Ax2 + Bx + C. (a) If A > 0, the parabola opens up.
(b) If A < 0, the parabola opens down.
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Figure 1.9 A revenue function.
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Figure 1.10 The graphs of y = f(x) and y = g(x) intersect at P and Q.
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Figure 1.11 The intersection of the graphs off(x) = 3x + 2 and g(x) = x2.
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Figure 1.12 Three polynomials of degree 3.
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Figure 1.13 Graphs of three rational functions.
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Figure 1.14 The vertical line test.
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Figure 1.15 The cost function C(x) = 50x + 200.
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Figure 1.16 .Slope12
12
xy
xxyy
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Figure 1.17 The line joining (–2, 5) and (3, –1).
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Figure 1.18 The direction and steepness of a line.
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Figure 1.19 Horizontal and vertical lines.
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Figure 1.20 The slope and y intercept of the liney = mx + b.
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Figure 1.21 The line 3y + 2x = 6.
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Figure 1.22 The line .23
21 xy
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Figure 1.23 The line y = –4x + 10.
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Figure 1.24 The rising price of bread: y = 2x + 136.
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Figure 1.25 Growth of federal civilian employment in the United States (1950–1989).
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Figure 1.26
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Figure 1.27 Lines parallel and perpendicularto a given line L.
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Figure 1.28 Rectangular picnic area.
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Figure 1.29 The length of fencing: .000,10)(x
xxF
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Figure 1.30 Cylindrical can for Example 4.2.
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Figure 1.31 The cost function: .966)( 2
rrrC
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r C(r)
0.5 608
1.0 320
1.5 243
2.0 226
2.5 238
3.0 270
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Figure 1.32 The cost of water in Marin County.
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x C(x)
0 0
12 14.64
24 134.64
30 434.64
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Figure 1.33 The rate of bounded population growth: R(p) = kp(b – p).
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Figure 1.34 The profit functionP(x) = (6,000 – 400x)(x – 2).
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Figure 1.35 Market equilibrium: the intersection of supply and demand.
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Figure 1.36 The supply and demand curvesfor Example 4.6.
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Figure 1.37 Geometric interpretation of the limit.
(a) If the height of
the graph of f approaches L as x approaches c.
,)(lim Lxfcx
(b) Geometric interpretation of the limit statement
31
22
lim1
x
xx
x
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Figure 1.38 Three functions for which .)(lim Lxfcx
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Figure 1.39 Two functions for whichdoes not exist.
)(lim xfcx
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Figure 1.40 Limits of two linear functions.
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Figure 1.41 The graph of .21)(
xxxf
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Figure 1.42 The graph of .23
1)( 2
2
xx
xxf
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Figure 1.43 Just in time inventory.
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Figure 1.44 The graph of .2if12
2if1)(
2
xx
xxxf
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Figure 1.45 A continuous graph.
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Figure 1.46 Three functions with discontinuities of x = c.
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Figure 1.47 Functions for Example 6.3.
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Figure 1.48 The graph of .32)(
xxxf
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Figure 1.49 The intermediate value property.
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Figure 1.50 The graph of .1
112
xxxy