Questions: Determine whether the equation defines y as a function of x.

Solution Steps

To determine whether the equation defines $y$ as a function of $x$, we need to check if for every $x$ there is exactly one $y$. This can be done by solving the equation for $y$ and checking if $y$ is uniquely determined by $x$.

We start with the equation $y^2 = x$.

To determine if $y$ is a function of $x$, we solve the equation for $y$: $$y = \pm \sqrt{x}$$

The solutions to the equation are $y = \sqrt{x}$ and $y = -\sqrt{x}$. This means for each $x$, there are two possible values of $y$.

Final Answer