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)

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.2 The composition f(g(x)) as an assembly line

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.3 (a) A production function. (b) Bounded population growth

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.4 (a) The graph of y = x 2. (b) Other graphs through the points in Example

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.5 The graph of f(x) = 1-2-5

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.6 The graph of f(x) = –x 2 + x

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.7 The graph of the function y = x 3 – x 2 – 6x

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.8 The graph of the parabola y = Ax 2 + Bx + C. (a) If A > 0, the parabola opens up. (b) If A < 0, the parabola opens down

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.9 A revenue function

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.10 The graphs of y = f(x) and y = g(x) intersect at P and Q

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.11 The intersection of the graphs of f(x) = 3x + 2 and g(x) = x

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.12 Three polynomials of degree

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.13 Graphs of three rational functions

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.14 The vertical line test

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.15 The cost function C(x) = 50x

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.17 The line joining (–2, 5) and (3, –1)

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.18 The direction and steepness of a line

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.19 Horizontal and vertical lines

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.20 The slope and y intercept of the line y = mx + b

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.21 The line 3y + 2x =

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.22 The line

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.23 The line y = –4x

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.24 The rising price of bread: y = 2x

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.25 Growth of federal civilian employment in the United States (1950–1989)

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.27 Lines parallel and perpendicular to a given line L

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.28 Rectangular picnic area

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.29 The length of fencing:

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.30 Cylindrical can for Example

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.31 The cost function: rC(r)

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.32 The cost of water in Marin County xC(x)

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.33 The rate of bounded population growth: R(p) = kp(b – p)

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.34 The profit function P(x) = (6,000 – 400x)(x – 2)

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.35 Market equilibrium: the intersection of supply and demand

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.36 The supply and demand curves for Example

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.37 Geometric interpretation of the limit. (a) If the height of the graph of f approaches L as x approaches c. (b) Geometric interpretation of the limit statement

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.38 Three functions for which

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.39 Two functions for which does not exist

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.40 Limits of two linear functions

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.41 The graph of

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.42 The graph of

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.43 Just in time inventory

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.44 The graph of

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.45 A continuous graph

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.46 Three functions with discontinuities of x = c

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.47 Functions for Example

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.48 The graph of

Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.49 The intermediate value property

Copyright © 2000 by the McGraw-Hill Companies, Inc Figure 1.50 The graph of