# Function topicExplain what is a function.

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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Basically a function is a relationship between variables in which one variable completely determines the value of the second variable.

In a function, whenever one variable has a certain value, the other variable must have some other specific value.

So let's say that we have the function f(x) = 3x.  If x = 3, f(x) must equal 9 -- f(x) is completely determined by the value of x.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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A function implies 3 elements: domain of the function, the codomain or the range of the values of the function and the relation between the variable x and y.

The values of x are located in the domain of the function.

Since y is a function of x, the range of values of y is determined by plugging in values to x in the given relation.

We'll consider the function f:R - >R

We'll assign an expression to f(x) = y:

y = 3x + 1

For each value of x, there is a single value for y.

For any value of x, from the domain