文档介绍：A graphical representation of a function––here the
number of hours of daylight as a function of the time
of year at various latitudes–– is often the most nat-
ural and convenient way to represent the function.
Functions and Models
The fundamental objects that we deal with in calculus are
functions. This chapter prepares the way for calculus by
discussing the basic ideas concerning functions, their
graphs, and ways of transforming bining them.
We stress that a function can be represented in different
ways: by an equation, in a table, by a graph, or in words. We look at the main
types of functions that occur in calculus and describe the process of using these func-
tions as mathematical models of real-world phenomena. We also discuss the use of
graphing calculators and graphing software puters.
|||| Four Ways to Represent a Function
Functions arise whenever one quantity depends on another. Consider the following four
situations.
A. The area A of a circle depends on the radius r of the circle. The rule that connects r
and A is given by the equation A r 2 . With each positive number r there is associ-
ated one value of A , and we say that A is a function of r.
Population B. The human population of the world P depends on the time t . The table gives estimates
͑͒
Year (millions) of the world population P t at time t, for certain years. For instance,
P͑1950͒Ϸ2,560,000,000
1900 1650
1910 1750 But for each value of the time t there is a corresponding value of P, and we say that
1920 1860 P is a function of t .
1930 2070
C. The cost C of mailing a first-class letter depends on the weight w of the letter.
1940 2300
Although there is no simple formula that connects w and C , the post office has a rule
1950 2560
for determining C when w is known.
1960 3040
1970 3710 D. The vertical acceleration a of the ground as measured by a seismograph during an
1980 4450 earthquake is a function of the elapsed time t. Figu