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Nos exercícios de 1 a 4, determine se a fórmula define y como uma função de x. Caso a resposta seja não, justifique. 

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.

Nos exercícios de 1 a 4, determine se a fórmula define y como uma função de x. Caso a resposta seja não, justifique.

Analyze four mathematical equations to determine if y is defined as a function of x. Learn about functions, inverse functions, and the reasoning behind each solution. This exercise covers algebraic concepts and is suitable for high school students.

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