Answer
The given equation is $2x+{{y}^{2}}=6$ does not define y as a function of x.
Work Step by Step
Let us the consider the following equation:
$2x+{{y}^{2}}=6$
Isolate y on the left in the above equation
$y=\sqrt{6-2x}$
The above equation will not provide a unique value of y for different values of x as there can be a negative as well as a positive value.
Apply the vertical line test according to which if any vertical line (parallel to the x-axis) intersect the provided graph into two different points then it is not a function.
The graph of the equation will be a left facing parabola so more than one vertical line will cross the graph in more than one point.
So, the above equation does not define y as a function of x.
