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.

C H A P T E R 1

Functions, Graphs, and Limits


Figure 1.1 Interpretations of the function f(x).

1-1-1


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.

1-2-8


Figure 1.9 A revenue function.

1-2-9


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.

1-2-13


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


Figure 1.32 The cost of water in Marin County.

1-4-32

x C(x)

0 0

12 14.64

24 134.64

30 434.64


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

1-5-37


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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copyright © 2000 by the mcgraw-hill companies, inc. c h a p t e r 1 functions, graphs, and limits

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