are parabolas that open to the right / left quadratic functions too?

Question

unklerhaukus · Answer

parabolas that open to the left are right are not functions,

they are relations

unklerhaukus · Answer

a function can only have a single output for the each input 

a test for this is the vertical line test, which say that on the graph of a relation, if any vertical line touches the line of the relation at more than one place the the relation is not a function 

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anonymous · Answer

THANK YOU, SO MUCH! ;D

unklerhaukus · Answer

i would say that $x=y^2$ is a quadratic relation though

unklerhaukus · Answer

kinda similar 
is
$$y=\sqrt x$$

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 which only has one output for each input 
and thus passes the vertical line test 
so $$y=\sqrt x$$ is a function

unklerhaukus · Answer

These relations are different so you'll have to remember to be carful if you want to rearrange the first relation 

$$y^2=x$$$$y=+\sqrt x,-\sqrt x$$$$\quad=±\sqrt x$$
which is clearly not a function as it has two values for most inputs