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The image presents the following mathematical question in Spanish:

**Question:**
"¿Qué tipo de función es la siguiente expresión analítica?"

The function is given as:
\[ f(x) = 5x^4 - 3x^2 \]

**Answer options:**
a) Función par  
b) Función lineal  
c) Función trigonométrica  
d) Función impar  

To determine the correct type of function, let's evaluate it.

### Analysis:
1. **Even function (Función par):**
   A function \( f(x) \) is called even if \( f(-x) = f(x) \) for all \( x \). Let's check:
   \[
   f(-x) = 5(-x)^4 - 3(-x)^2 = 5x^4 - 3x^2 = f(x)
   \]
   Hence, \( f(x) \) is an **even function**.

2. **Linear function (Función lineal):**
   A linear function has the form \( f(x) = mx + b \), but this function has higher degree terms (degree 4 and degree 2), so it is **not linear**.

3. **Trigonometric function (Función trigonométrica):**
   A trigonometric function involves terms like \( \sin(x), \cos(x), \tan(x) \), etc. This function does not involve any trigonometric terms, so it is **not trigonometric**.

4. **Odd function (Función impar):**
   A function \( f(x) \) is called odd if \( f(-x) = -f(x) \). In this case, we already checked that \( f(-x) = f(x) \), so it is **not odd**.

### Conclusion:
The function \( f(x) = 5x^4 - 3x^2 \) is an **even function (Función par)**, so the correct answer is **option a)**.

Let me know if you'd like more details or if you have any questions!

Here are some related questions to deepen understanding:
1. How can we determine if a function is odd or even using a graph?
2. What are the main characteristics of a linear function?
3. What distinguishes a trigonometric function from a polynomial function?
4. Can a function be both even and odd? Why or why not?
5. How do the degrees of the terms in a polynomial affect whether it is even or odd?

**Tip:** A quick way to identify even functions is by checking if all the powers of \( x \) in the expression are even, as in this case (degree 4 and degree 2).

¿Qué tipo de función es la siguiente expresión analítica? f(x) = 5x^4 - 3x^2

Analyze the function f(x) = 5x^4 - 3x^2 to determine whether it is an even, odd, or neither function. This problem involves key concepts from algebra and polynomial functions, suited for high school students.

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