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Oct 11, 2015 · Roughly speaking, a variable is a symbol for which one substitutes names for some objects, usually a number in algebra. A variable is always associated with a set of objects whose names can be substituted for it. These objects are called values of the variable. (p. 70)
Originally, the term "variable" was used primarily for the argument of a function, in which case its value can vary in the domain of the function. This is the motivation for the choice of the term. Also, variables are used for denoting values of functions, such as y in.
Jun 25, 2020 · The confusion arises because there are two inconsistent, albeit related, uses of the word function. The older use is what may be called a dependent variable , in (for example) the phrase “ $y$ is a function of $x$ ” or, more specifically, “the function $y=2x+4$ ”.
Nov 26, 2024 · For example, the variables in the function f (x,y) are x and y. A function having a single variable is said to be univariate, one having two variables is said to be bivariate, and one having two or more variables is said to be multivariate.
For example, a function f can be defined as mapping any pair of real numbers (,) to the sum of their squares, +. Such a function is commonly written as (,) = + and referred to as "a function of two variables".
Definition 1 A function f of the two variables x and y is a rule that assigns a number f(x, y) to each point (x, y) in a portion or all of the xy-plane. f(x, y) is the value of the function at (x, y), and the set of points where the function is defined is called its domain.
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Functions of two variables can be described numerically (a table), graphically, algebraically (a formula), or in English. We will often now call the familiar \(y = f(x)\) a function of one variable.
