Special names are commonly used for such powers from one to five-linear, quadratic, cubic, quartic, and quintic for the highest powers being 1, 2, 3, 4, and 5, respectively. Polynomial functions are characterized by the highest power of the independent variable. (When the powers of x can be any real number, the result is known as an algebraic function.) Polynomial functions have been studied since the earliest times because of their versatility-practically any relationship involving real numbers can be closely approximated by a polynomial function. The general form for such functions is P( x) = a 0 + a 1 x + a 2 x 2+⋯+ a n x n, where the coefficients ( a 0, a 1, a 2,…, a n) are given, x can be any real number, and all the powers of x are counting numbers (1, 2, 3,…). The formula for the area of a circle is an example of a polynomial function. Get a Britannica Premium subscription and gain access to exclusive content. In addition to f( x), other abbreviated symbols such as g( x) and P( x) are often used to represent functions of the independent variable x, especially when the nature of the function is unknown or unspecified. The set of values of x is called the domain of the function, and the set of values of f( x) generated by the values in the domain is called the range of the function. To use the language of set theory, a function relates an element x to an element f( x) in another set. That is, f( x) can not have more than one value for the same x.
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This relationship is commonly symbolized as y = f( x)-which is said “ f of x”-and y and x are related such that for every x, there is a unique value of y.
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If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of y is determined, then y is said to be a function of the independent variable x. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet: Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.
#Function mathematica how to
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Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.G.9) Interpolation and approximation Here is a plot of f- Vx for 0 sx s 10 Clear[f, x f[x sort x fplot 3.0 2.5 2.0 1.5 0. After observing the graphs, the goal is to come up with three new points so that when you add the three new points to the list above, the plot of runner will be as close as you can make it to the plot of f.