Let's analyze each equation to determine if $y$ is defined as a function of $x$. A function implies that for every $x$, there is only one corresponding value of $y$.

1. $y = \sqrt{x - 4}$:
   This equation defines $y$ as a function of $x$, because for each value of $x \geq 4$, there is only one corresponding value for $y$ (the non-negative square root).

2. $y = x^2 + 3$:
   This is also a function of $x$, because for each $x$, there is exactly one value of $y$.

3. $x = 2y^2$:
   Here, $y$ is not defined as a function of $x$. If we solve for $y$, we get $y = \pm \sqrt{\frac{x}{2}}$, meaning that for some values of $x$, there are two possible values of $y$. Hence, it is not a function.

4. $x = 12 - y$:
   Solving for $y$ gives $y = 12 - x$. This defines $y$ as a function of $x$, since for each value of $x$, there is only one corresponding value for $y$.

Summary:

• Equation 1: Function
• Equation 2: Function
• Equation 3: Not a function (since there are two possible values of $y$ for some $x$)
• Equation 4: Function

Would you like any further details or explanations?

Here are 5 related questions:

1. What is the formal definition of a function in terms of sets?
2. Can $y = \pm \sqrt{x}$ ever define $y$ as a function of $x$?
3. How would the domain of each function be determined?
4. Could the equation $x = y^2$ be modified to define $y$ as a function of $x$?
5. In which cases can an equation involving squares define a function?

Tip: When determining if an equation defines a function, always check if every $x$-value corresponds to exactly one $y$-value.