Well is y = sqrt(x) a function?

I understand the definition of a function but I wonder this since when you simply graph y = sqrt(x) in a calculator it only shows the positive y values and will only give the negative ones if you also input y = -sqrt(x).

Shouldn't y=sqrt(x) in reality contain both the positive and negative y values since sqrt give a positive and negative answer?

I assume the calculator only graphs the positive values since that is just how it works. Or when given y=sqrt(x). Are we only supposed to show the positive values unless given -sqrt(x)?

I'm sorry if this post is poorly worded. Hopefully someone will understand what I am saying.