Search results
- DictionaryFunc·tion/ˈfəNG(k)SHən/
noun
- 1. an activity or purpose natural to or intended for a person or thing: "bridges perform the function of providing access across water"
- 2. a relationship 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"
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.
Learn the meaning of function as a noun and a verb in different contexts, such as purpose, ceremony, work, mathematics, and computing. See how to use function in sentences and phrases with synonyms and related words.
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
- So, one day, I asked my dad if a function could be graphed as a circle. He said yes. But I said no b...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...
- at 7:26 why is y a square root of three? why not 3 squared?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,...
- I don't get how Sal got h(2)=3 and h(8)=11. someone help please?_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...
- why are there two variables?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...
- Can a function have multiple inputs? If so, how would you graph said function?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...
- Hi! I was wondering if there is a relationship between the equation describing how to plot a circle ...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...
- What does the f stand for?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...
- How can we graph the fancy function h(a)?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...
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
- GeneratedCaptionsTabForHeroSec
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.
Special offer for students! Check out our special academic rate and excel this spring semester!
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 their applications in mathematics and science.
- The Editors of Encyclopaedia Britannica
Functions are often defined by an expression that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Learn the meaning of function as a noun and a verb, with different senses and usage. Find out how to use function in sentences and phrases, and see translations in other languages.
