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From the image you uploaded, we are tasked with determining whether the given functions are **even**, **odd**, or **neither** based on their graphs or equations.

### 1. **The function \( r \) (graph on the left)**:
- The graph of \( r \) is a straight line with a negative slope, indicating a linear function.
- A function is **odd** if \( f(-x) = -f(x) \), and linear functions of the form \( f(x) = mx + b \) (where \( m \neq 0 \) and \( b = 0 \)) are odd.
- Since the line passes through the origin and has a negative slope, this function is **odd**.

### 2. **The function \( s \) (graph on the right)**:
- The graph of \( s \) appears symmetric with respect to the y-axis.
- A function is **even** if \( f(-x) = f(x) \). This symmetry suggests that \( s(x) \) satisfies the condition for being even.
- Therefore, the function \( s \) is **even**.

### 3. **The function \( g(x) = -2x^5 + 3x^2 \)**:
- To determine if the function is even, odd, or neither, check its terms:
  - \( x^5 \) is an odd power, and \( x^2 \) is an even power.
  - The term \( -2x^5 \) is odd, and \( 3x^2 \) is even.
- Since this function contains both even and odd powers of \( x \), it is **neither** even nor odd.

### 4. **The function \( h(x) = -6x^5 + 3x^3 \)**:
- Both terms in \( h(x) \) are odd powers of \( x \) (i.e., \( x^5 \) and \( x^3 \)).
- A function composed entirely of odd powers with coefficients behaves like an odd function, as \( f(-x) = -f(x) \) holds for each term.
- Therefore, the function \( h(x) \) is **odd**.

### Summary:
- Function \( r \): **Odd**
- Function \( s \): **Even**
- Function \( g(x) = -2x^5 + 3x^2 \): **Neither**
- Function \( h(x) = -6x^5 + 3x^3 \): **Odd**

Would you like more details on any of these? Here are some related questions:

1. How can you determine if a function is even from its equation alone?
2. What are the geometric properties of even and odd functions?
3. Why is a function with mixed even and odd powers (like \( g(x) \)) considered neither even nor odd?
4. How do transformations like shifts affect whether a function is even or odd?
5. What is the significance of symmetry in determining whether a function is even or odd?

**Tip**: Always check the behavior of a function by substituting \( x \) with \( -x \) to determine if it's even, odd, or neither!

Determine whether the given functions are even, odd, or neither based on their graphs or equations.

Learn how to determine whether a function is even, odd, or neither by analyzing its graph and equation. This problem covers key algebraic concepts, including symmetry and the properties of even and odd functions. Suitable for high school students (Grades 9-12).

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