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The task in the image involves calculating values for different mathematical functions and determining whether each function is odd, even, or neither. Let's solve the functions for the given values of \( x \) and then determine the nature of each function.

### 1. Polynomial Function: \( f(x) = 2x^2 + 3 \)

**Calculations:**
- For \( x = -2, 0, 1, 3, 5 \)

### 2. Trigonometric Function: \( f(x) = 4\sin(x) + 1 \)

**Calculations:**
- For \( x = -\pi, -1, 0, 1, \pi \)

### 3. Cubic Function: \( f(x) = 2x^5 + 3x \)

**Calculations:**
- For \( x = -3, -2, -1, 0, 2 \)

### Nature Determination:
- **Odd Function:** \( f(-x) = -f(x) \)
- **Even Function:** \( f(-x) = f(x) \)

Let's compute the necessary values and determine the nature of these functions.Here are the calculated values for each function:

### 1. Polynomial Function: \( f(x) = 2x^2 + 3 \)
- For \( x = -2, 0, 1, 3, 5 \), the values of \( y \) are \([11, 3, 5, 21, 53]\) respectively.

### 2. Trigonometric Function: \( f(x) = 4\sin(x)

Fill out the table of values and select whether each function is odd, even, or neither. The functions provided are f(x) = 2x^2 + 3, f(x) = 4sin(x) + 1, and f(x) = 2x^5 + 3x.

This problem involves determining whether given functions such as f(x) = 2x^2 + 3, f(x) = 4sin(x) + 1, and f(x) = 2x^5 + 3x are odd, even, or neither. The problem covers key concepts in trigonometry, polynomials, and function analysis, with table-based calculations.

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