Let's analyze the given functions to determine whether each is even, odd, or neither:

1. The function $r$ (top-left graph):

• Observation: The graph of $r$ does not exhibit symmetry around either the y-axis (required for an even function) or the origin (required for an odd function).
• Conclusion: The function $r$ is neither even nor odd.

2. The function $s$ (top-right graph):

• Observation: The graph of $s$ is symmetric about the y-axis, meaning that for every $x$, $s(-x) = s(x)$.
• Conclusion: The function $s$ is even.

3. The function $g(x) = -6x^5 + 7x^3$ (bottom-left equation):

• Observation: All powers of $x$ in the function are odd, which suggests that $g(-x) = -g(x)$.
• Conclusion: The function $g(x)$ is odd.

4. The function $h(x) = -6x^5 + 3x^2$ (bottom-right equation):

• Observation: The function contains both odd (5th degree) and even (2nd degree) powers of $x$, which suggests that $h(x)$ does not satisfy the conditions for being either even or odd.
• Conclusion: The function $h(x)$ is neither even nor odd.

Would you like any further details or explanations?

Here are 5 related questions to further explore this topic:

1. What is the mathematical definition of an even function?
2. What conditions must be met for a function to be classified as odd?
3. How can you algebraically verify whether a function is even, odd, or neither?
4. Why does symmetry about the y-axis correspond to an even function?
5. Can a function be both even and odd?

Tip: For functions defined explicitly, like $g(x)$ or $h(x)$, you can check their parity by substituting $-x$ for $x$ and simplifying.