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Let's address the questions one by one.

### Question 2:
**Indica si las siguientes expresiones son o no una función. ¿Se trata de un polinomio? Sí, no, ¿por qué? En caso de serlo, ¿cuál es el grado del polinomio?**

Let’s analyze each part:

**a. \( 3x^2 - 4y = 1 \)**
- Rearranged, this can be written as \( y = \frac{3x^2 - 1}{4} \). This is a function since for each value of \( x \), there is exactly one value for \( y \). 
- It is a polynomial of degree 2.

**b. \( y - 2 \cos \left( 2x - \frac{\pi}{3} \right) + 4 = 0 \)**
- Rearranged: \( y = 2 \cos \left( 2x - \frac{\pi}{3} \right) - 4 \). This is a trigonometric function, not a polynomial because cosine is not a polynomial.

**c. \( k(x) = \sqrt{2x - 1} \sqrt{3x + 2} \)**
- This is a square root function, not a polynomial because it involves roots.

**d. \( 2y = \sqrt{x - 7} \)**
- Rearranged: \( y = \frac{\sqrt{x - 7}}{2} \). This is a square root function, not a polynomial.

**e. \( y = \frac{3x - 6}{x^2} \)**
- This is a rational function, not a polynomial because it involves division by \( x^2 \).

**f. \( y(x) = \frac{1}{x^2 - 4} \)**
- This is a rational function because it involves division by a polynomial, so it’s not a polynomial.

**g. \( x^2 + 12x + 7 + y^2 - 43 = 0 \)**
- Rearranged: \( y^2 = -x^2 - 12x - 7 + 43 \), then \( y = \pm \sqrt{(x^2 + 12x + 36)} \). This is not a function because for each \( x \), there are two values of \( y \) (plus and minus).

**h. \( f(x) = \sqrt{x^2 - 2} \)**
- This is a square root function, not a polynomial.

**i. \( g(x) = \frac{\sqrt{x^2 - 2x + 1}}{4} \)**
- This simplifies to \( g(x) = \frac{|x-1|}{4} \). This is an absolute value function, not a polynomial.

### Question 3:
**Encuentra sus raíces o ceros, dominio, rango y realiza su gráfica para las siguientes funciones:**

We are given several polynomials, and for each, we are required to find:

1. **Raíces o ceros (roots or zeros)**
2. **Dominio (domain)**
3. **Rango (range)**
4. **Graph of the function**

The polynomials listed are:
- \( P(x) = x^2 - 6x + 9 \)
- \( P(x) = 3x^2 + 5x - 2 \)
- \( P(x) = -x^2 + 5x - 4 \)
- \( P(x) = 4x^2 + 2 \)
- \( P(x) = 2x^2 + 5x - 3 \)
- \( P(x) = x^2 + 4x + 6 \)
- \( P(x) = x^2 - 5x \)
- \( P(x) = -x^2 - 2x - 3 \)
- \( P(x) = x^2 - 5x - 4 \)

If you want, we can go step by step and solve for one or multiple polynomials, finding their zeros, domain, and range.

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Let me know if you'd like detailed solutions for any specific polynomial from Question 3, or if you'd like further clarifications on Question 2. 

### Related questions:
1. How do you determine if an equation is a polynomial?
2. What are the steps to find the domain of a rational function?
3. How do trigonometric and square root functions differ from polynomials?
4. Can you explain how to find the range of a quadratic function?
5. What is the significance of roots or zeros in a polynomial?

**Tip:** Always rearrange the equation into \( y = f(x) \) form to clearly analyze if it's a function.

Indica si las siguientes expresiones son o no una función. ¿Se trata de un polinomio? Sí, no, ¿por qué? En caso de serlo, ¿cuál es el grado del polinomio? Encuentra sus raíces o ceros, dominio, rango y por último realiza su grafica la función.

Understand how to determine whether given mathematical expressions are functions or polynomials, and learn how to find the roots, domain, range, and graph for various functions. Includes analysis of trigonometric, rational, square root, and absolute value functions, suitable for high school math students.

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