There are a number of important types of functions frequently encountered in calculus. We
identify and briefly summarize them here.
Linear Functions A function of the form for constants m and b, is
called a linear function. Figure 1.34 shows an array of lines where so
these lines pass through the origin. Constant functions result when the slope
Power Functions A function where a is a constant, is called a power function.
There are several important cases to consider.
(a)
The graphs of for 2, 3, 4, 5, are displayed in Figure 1.36. These functions
are defined for all real values of x. Notice that as the power n gets larger, the curves
tend to flatten toward the x-axis on the interval and also rise more steeply for
ƒ x ƒ 7 1. Each curve passes through the point (1, 1) and through the origin.
s -1, 1d,
ƒsxd = xn , n = 1,
a = n, a positive integer.
ƒsxd
Polynomials A function p is a polynomial if
where n is a nonnegative integer and the numbers are real constants
(called the coefficients of the polynomial). All polynomials have domain If
the leading coefficient and then n is called the degree of the polynomial.
Linear functions with are polynomials of degree 1. Polynomials of degree 2, usually
written as are called quadratic functions. Likewise, cubic
functions are polynomials of degree 3. Figure 1.39 shows
the graphs of three polynomials. You will learn how to graph polynomials in
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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