Explanation:
y² = x
is a quadratic equation (parabola) on y instead of usually in x.
that makes it a parabola that opens sideways (instead of upwards or downwards). in this case it opens to the right starting with x = 0.
to form it back to our usual y = ... format we see
y² = x
corresponds to
y = ±sqrt(x)
and there we see immediately that for (almost) every x there are 2 y-values associated (instead of 1, which is the necessary condition to be a function) : e.g. ±1 for x = 1, ±2 for x = 4, ...
so, Francesca is NOT correct. it is NOT a function.
she just tested the one point of that (x, y) relation, for which the function criteria seems to be true : the vertex at (0, 0).
but for every other positive x it is not true.
she needs to do the vertical line test with various vertical lines to see if there are more than one intersections with the relation.