Is √y = |x| a function? And why?

Answer 1

Maddie,

First let us rewrite this as

y = lxl²

That is, y is equal to the absolute value of x, squared.

This is a function. Remember that being a function just means that any x value should give only one specific y value. If we have points (1,2) and (1,4) for example, that is not a function because if we can have different y-values for the same x value, y is clearly not determined by x (aka, y is clearly not a FUNCTION of x). However, it is fine if different x values give the same y value, like points (1,2) and (2,2).

In this particular function, plugging in any specific x value will give you only one specific y value. If x = 2 for example, y will always be one specific value (it will always be 4). So y is clearly determined by x, which means it is a function of x.

Hope this helps! :)