Final answer:
An odd function is symmetric with respect to the origin and passes through two points (-3, 21) and (-3, -5). Using the slope formula, we find that the slope is undefined.
Step-by-step explanation:
An odd function is symmetric with respect to the origin, meaning that for every point (x, y) on the graph of the function, the point (-x, -y) is also on the graph. Since f is an odd function and f(3) = 5, we can conclude that f(-3) = -5. This is because (-3, -5) is the reflection of (3, 5) across the origin.
Therefore, the curve of the function passes through the point (-3, 21) and (-3, -5). To find the slope between these two points, we can use the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-3, 21) and (x2, y2) = (-3, -5).
Substituting the values, we get:
m = (-5 - 21) / (-3 - (-3)) = -26 / 0 = old{undefined}