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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:

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: f(x,y) = x2 + 3y, then x,y are said to be the variables of the function, f.

Further, f(1,2) = (1)2 + 3(2) = 1 + 6 = 7. 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: f(x,y) = x2 + ay, then a 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.

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