# How do you decide whether the relation #x = y^2 - 2y + 1# defines a function?

##### 1 Answer

Nov 27, 2015

This relation is not a function.

#### Explanation:

Your relation is not a function.

The reason for this is that you can find an

Let's transform the right side a bit so that it's easier to see:

Now, if this relationship was a function, you would need to obtain one unique ("one and only one") value for

However, this doesn't hold here:

E.g., for

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Another way to see this is to graph the function:

graph{x = y^2 - 2y + 1 [-5, 15, -5, 5]}

Here, you also see very clearly that:

- the function is not defined for
#x <0# , - for
#x = 0# it has indeed one unique value for#y# , - and for
#x > 0# , each#x# has two#y# values.