# What are functions?

Functions are mathematical expressions describing the relationship between variables and involve only algebraic operations. If there is one independent variable, the dependent variable, for example y, can be determined through the function. This is often seen written as y = f(x), spoken as, “y equals fof x” (functions also use notation with x; for example, f(x) = 2x + 1 is a function). Functions within equations are also common; for example, in the equation -x2 + y = 3, the y represents a function of x. To see this, note that this equation can also be written as y = 3 + x2.

Functions do not always have to be in terms of f(x). They can just as easily be termed g(x), depending on the equation. But note: The equation x2 + y2 = 9 is not a function, as x and yare both independent variables.

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