Difference between revisions of "Variable"
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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: |
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| + | Given: | ||
| + | 5 + x = 12 | ||
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| + | Find x. | ||
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| + | Since 5 + 7 = 12, the answer is: | ||
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| + | x = 7 | ||
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| + | 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>. | ||
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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 | + | 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]] |
Latest revision as of 02:47, September 7, 2017
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: 
, then 
are said to be the variables of the function, 
.
Further, 
. 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: 
, then 
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.
