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The question asks which of the given expressions represents a function. Let's analyze each one:

### a) \( y = 2x + 1 \)
This is a linear equation. For every \( x \), there is exactly one corresponding \( y \). Hence, **this is a function**.

### b) \( y = \{(2, y) \mid y \in \mathbb{N}\} \)
This set describes a relation where \( x = 2 \), but it doesn't explicitly define a unique \( y \) for each \( x \). Instead, it implies multiple values of \( y \) for \( x = 2 \), which means it **does not represent a function**.

### c) \( f = \{(x, 2) \mid x \in \mathbb{Z}\} \)
This defines a set of ordered pairs where the second element is always 2, regardless of \( x \). Every \( x \) in \( \mathbb{Z} \) corresponds to exactly one value of \( y = 2 \), so **this is a function**.

### d) \( y = \pm \sqrt{2x + 2} \)
The symbol \( \pm \) indicates two possible values for each \( x \), which means there are two values of \( y \) for one \( x \). Therefore, this expression **does not represent a function**.

### e) \( y = +\sqrt{x - 3} \)
This expression involves the square root of \( x - 3 \), but it only considers the positive square root. For every valid \( x \geq 3 \), there is only one value of \( y \), making this **a function**.

### f) \( f = \{(x, x + 2) \mid x \in \mathbb{N}\} \)
This defines a set of ordered pairs where each \( x \) corresponds to exactly one value \( x + 2 \). Since there is a unique \( y \) for every \( x \), **this is a function**.

### Final Answer:
The following expressions represent functions:
- \( a \), \( c \), \( e \), and \( f \).

Would you like more details on any part of this? Here are five related questions you might explore:
1. What is the formal definition of a function?
2. Can a relation with multiple \( y \)-values for a single \( x \)-value be a function?
3. How can we graphically represent a function and a non-function?
4. Why is the expression \( y = \pm \sqrt{2x + 2} \) not a function?
5. How do we define functions with set notation, like in option \( b \)?

**Tip:** When determining whether an expression represents a function, remember that each \( x \)-value must map to exactly one \( y \)-value.

¿Cuál de las siguientes expresiones representa una función?

Explore which expressions represent functions based on algebraic formulas and set notation. This problem covers concepts such as linear equations, square root functions, and the formal definition of a function. Suitable for high school students in Grades 9-12.

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