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