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In mathematics, a variable is a value which usually is the subject or part of a [[function]] and must be subject to change while not affecting the structure behind the function in which it acts.
In mathematics, a '''variable''' is a number whose value is not known. In basic arithmetic problems, the variable is typically the answer which the student must find:
Given:
5 + x = 12
Find x.
Since 5 + 7 = 12, the answer is:
x = 7
A variable is usually is the subject or part of a [[function]] and must be subject to change while not affecting the structure behind the function in which it acts.
For example, if we have a function: <math>f(x,y)=x^{2}+3y</math>, then <math>x,y</math> are said to be the variables of the function, <math>f</math>.
For example, if we have a function: <math>f(x,y)=x^{2}+3y</math>, then <math>x,y</math> are said to be the variables of the function, <math>f</math>.
Further, <math>f(1,2)=(1)^{2}+3(2)=1+6=7</math>. We change the variable and thus alter the value of the function.
Further, <math>f(1,2)=(1)^{2}+3(2)=1+6=7</math>. We change the variable and thus alter the value of the function.
Sometimes a function can have also a [[parameter]]. A parameter is similar to a variable, but is not written like a variable and is thus more similar to a [[constant]]. For example, if we a function: <math>f(x,y) = x^2 + ay</math>, then <math>a</math> is said to be a [[parameter]]. It does not change like the variables x and y, but it can nonetheless take different values. It is important to clearly distinguish the two concepts.
The [[set]] of all variables upon which a function acts is said to be the [[domain]]. The set of all values that a function can take due to its domain is called its [[range]].
The [[set]] of all variables upon which a function acts is said to be the [[domain]]. The set of all values that a function can take due to its domain is called its [[range]].
[[Category:Mathematics]]