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- Dictionaryfunction/ˈfʌŋ(k)ʃn/
noun
- 1. an activity that is natural to or the purpose of a person or thing: "bridges perform the function of providing access across water" Similar
- 2. a relation or expression involving one or more variables: "the function (bx + c)"
verb
- 1. work or operate in a proper or particular way: "her liver is functioning normally" Similar Opposite
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something that results from something else, or is the way it is because of something else: His success is a function of his having worked so hard.
Learn the various meanings and uses of the word function as a noun and a verb, with synonyms, examples, and etymology. Find out how function relates to mathematics, biology, chemistry, and computer science.
Function definition: the kind of action or activity proper to a person, thing, or institution; the purpose for which something is designed or exists; role.. See examples of FUNCTION used in a sentence.
- Overview
- Common functions
- Complex functions
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function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet:
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.
Many widely used mathematical formulas are expressions of known functions. For example, the formula for the area of a circle, A = πr2, gives the dependent variable A (the area) as a function of the independent variable r (the radius). Functions involving more than two variables (called multivariable or multivariate functions) also are common in mathematics, as can be seen in the formula for the area of a triangle, A = bh/2, which defines A as a function of both b (base) and h (height). In these examples, physical constraints force the independent variables to be positive numbers. When the independent variables are also allowed to take on negative values—thus, any real number—the functions are known as real-valued functions.
Britannica Quiz
Numbers and Mathematics
The formula for the area of a circle is an example of a polynomial function. The general form for such functions is P(x) = a0 + a1x + a2x2+⋯+ anxn, where the coefficients (a0, a1, a2,…, an) are given, x can be any real number, and all the powers of x are counting numbers (1, 2, 3,…). (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. Polynomial functions are characterized by the highest power of the independent variable. 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 may be given geometric representation by means of analytic geometry. The independent variable x is plotted along the x-axis (a horizontal line), and the dependent variable y is plotted along the y-axis (a vertical line). When the graph of a relation between x and y is plotted in the x-y plane, the relation is a function if a vertical line always passes through only one point of the graphed curve; that is, there would be only one point f(x) corresponding to each x, which is the definition of a function. The graph of the function then consists of the points with coordinates (x, y) where y = f(x). For example, the graph of the cubic equation f(x) = x3 − 3x + 2 is shown in the figure.
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Practical applications of functions whose variables are complex numbers are not so easy to illustrate, but they are nevertheless very extensive. They occur, for example, in electrical engineering and aerodynamics. If the complex variable is represented in the form z = x + iy, where i is the imaginary unit (the square root of −1) and x and y are rea...
A function is a rule that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Learn about different types of functions, such as polynomial, trigonometric, exponential, and complex, and how they are used in mathematics and science.
- The Editors of Encyclopaedia Britannica
Learn the definition and examples of functions in algebra and programming. Watch a video and read the questions and answers from other learners about functions.
- 8 min
- Sal Khan
- Ωπ fαz919 πΩ , By definition of a function, a circle cannot be a solution to a function. A function, by definition, can only have one output value...
- You have to remember that in algebra, what is done to one side of the equation has to also be done to the other side of the equation. When y^2 = 3,...
- They are very similar. I think the best way to put it is that a math function takes in some mathematical construct (be it a number or some other va...
- _The next largest number that starts with the same letter as_ 2 is 3. They both start with the letter t. In the same way, _The next largest number...
- If you mean, "why does f(x) contain two variables?", please note the f is not a variable. The f is just a way for you to know that when you see f(x...
- Yes, a function can have multiple inputs. We can graph in the coordinate plane when we have 1 input to 1 output. If we have a function with 2 input...
- Yep, there definitely is. Let's consider a circle with center (0, 0) (to make the explanation a little simpler) and radius 3. Let's find some point...
- Basically, the concept of functions gives us a way to name the whole process of evaluating a particular expression, so we can talk about it as a wh...
- Good question, but, we need more info! For essence 'h (a) = x*a + b', where 'x' is the slope of the function and 'b' is the Y-axis intersection, or...
Learn the various meanings and uses of the word function in English, from grammar to mathematics to computer science. Find synonyms, examples, pronunciation and word frequency of function.
Learn the concept of a function in maths, algebra and graph, with examples and types. A function is a relation between inputs and outputs, where each input has only one output.
