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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.As we have seen in examples above, we can represent a function using a graph. Graphs display many input-output pairs in a small space. ... The most common graphs name the input value x and the output value y , and we say y is a function of x , or y=f(x) y = f ( x ) when the function is named f .

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