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Let's solve these two problems based on the uploaded images.

### Problem 1: Function from the Graph
You are asked to determine if the function shown in the graph is even, odd, or neither. Let's go step-by-step:

- **Even Function**: Symmetric about the y-axis, i.e., \( f(x) = f(-x) \).
- **Odd Function**: Symmetric about the origin, i.e., \( f(-x) = -f(x) \).
- **Neither**: If neither of these conditions hold.

#### Analyzing the Graph:
- For \( x = -3 \), \( f(-3) = 0 \) and for \( x = 3 \), \( f(3) = 0 \). This indicates symmetry for these points.
- However, at \( x = -1 \), \( f(-1) = 1 \), but at \( x = 1 \), \( f(1) = -2 \). Since these values are not equal, the function is not even.
- To check if it’s odd, we compare the values at \( x = -1 \) and \( x = 1 \). For \( x = -1 \), \( f(-1) = 1 \), but \( f(1) = -2 \), which does not satisfy \( f(-x) = -f(x) \). Thus, it is not odd either.

**Conclusion**: The function is **neither** even nor odd.

Other parts of the question:
- **First interval increasing**: From \( (-3, -1) \), the graph is increasing.
- **First interval decreasing**: From \( (0, 1) \), the graph is decreasing.
- **First interval constant**: From \( (-4, -3) \), the graph is constant.

### Problem 2: Identifying Odd Functions
An odd function satisfies \( f(-x) = -f(x) \). Let's analyze each function:

1. \( f(x) = |x| + x^2 \) 
   - This is **not odd** since \( |x| \) is neither odd nor even, and \( x^2 \) is even.
  
2. \( m(x) = |x| + x^3 \)
   - This is **not odd** because \( |x| \) is not odd, and although \( x^3 \) is odd, their combination isn't.

3. \( n(x) = 5 \)
   - Constant functions are **neither odd nor even**.

4. \( b(x) = 5x^3 + 2x^2 + 4x + 6 \)
   - Since the even-powered terms and constant terms don't satisfy \( f(-x) = -f(x) \), this function is **not odd**.

5. \( h(x) = 3x^4 - 5x^2 + 9 \)
   - This function is composed of even powers of \( x \), making it **even**, not odd.

6. \( c(x) = \frac{4x^2 + 2}{3x^3 - 5x} \)
   - Check if the function behaves like an odd function: substituting \( -x \) doesn’t result in \( -f(x) \), so it's **not odd**.

7. \( g(x) = 4x^7 + 2x^3 - x \)
   - All terms have odd powers of \( x \), so this function **is odd**.

**Conclusion**: The only odd function in this list is \( g(x) = 4x^7 + 2x^3 - x \).

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Let me know if you need more details on any part! Here are some additional questions you might explore:

1. What properties make a function even, odd, or neither?
2. Can a function be both even and odd? If so, under what circumstances?
3. How can we use symmetry to quickly identify even and odd functions?
4. What happens to the behavior of a function when you add an odd term to an even function?
5. How do transformations like reflections and translations affect the evenness or oddness of a function?

**Tip**: For graphical analysis, always check the symmetry by comparing corresponding points on opposite sides of the y-axis and origin.

Using the graph, determine if the function is even, odd, or neither. Additionally, solve for the first increasing, decreasing, and constant intervals. Choose all odd functions from the provided list of functions.

Learn how to determine if a function is even, odd, or neither based on a graph. Analyze the first increasing, decreasing, and constant intervals. Identify odd functions from a list using key properties of symmetry.

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