# Why is this a function? Domain (-2,-1,1/2,3) Range (2)

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### 2 Answers

A function is a relation between two sets of numbers such that every value in the set corresponding to the input, which is called the domain, has only one value in the set corresponding to the output, which is called the range.

In the function given in the problem all values in the domain {-2, -1, 1/2, 3} have one value in the range {2}. This is a constant function for the given values and can be written as: f(x) = 2.

One of the main characteristics of a function is that a value of y cannot have more than one corresponding value of x. According to the function given to you, this condition is met, as no numbers are repeated within the domain. A shortcut to finding out if you've got a function on your hands is to check for any repeated numbers in the domain. If you don't have any, then you're good, it's a function. If you do, then it's not.