To solve this problem, let's understand what it means for a function to be odd. If $f(x)$ is an odd function, it satisfies the property:

$f(-x) = -f(x)$

The points given are $(-5, -2)$ and $(3, 6)$.

Solution Steps:

1. Find $f(5)$:

   • Since $(-5, -2)$ is a point on the graph of $f$, we have $f(-5) = -2$.
   • Using the property of odd functions, $f(5) = -f(-5)$.
   • Therefore, $f(5) = -(-2) = 2$.

2. Find $f(-3)$:

   • Since $(3, 6)$ is a point on the graph of $f$, we have $f(3) = 6$.
   • Using the odd function property, $f(-3) = -f(3)$.
   • Therefore, $f(-3) = -6$.

Answer:

$f(5) = 2 \quad \text{and} \quad f(-3) = -6$

Would you like more details on any part of this solution?

Here are five related questions to explore further:

1. What defines an even function, and how does it differ from an odd function?
2. If the function were even instead of odd, what would the values of $f(5)$ and $f(-3)$ be?
3. How does symmetry play a role in identifying odd and even functions on a graph?
4. Can a function be both odd and even? If so, what type of function would that be?
5. How would we determine values for a function that is neither odd nor even?

Tip: Remember, odd functions are symmetric with respect to the origin, while even functions are symmetric about the y-axis.