Answer
$\text{$y$ is NOT a function of $x$.}$
Work Step by Step
For an equation to be a function: any input $x$ will yield only one output $y$
We start by solving the equation for $y$
Rearranging the equation:
$$3y^2=1-2x^2$$
Dividing both sides by $3$:
$$y^2=\dfrac{1-2x^2}{3}$$
Taking the square root of both sides:
$$y = \pm \sqrt{\dfrac{1-2x^2}{3}}$$
If $x=0$
$$y = \pm \sqrt{\dfrac{1-2(0)^2}{3}} = \pm \dfrac{\sqrt{3}}{3}$$
As there are two different outputs resulting from the same input, the equation isn't a function
