Final answer:
For an odd function, if (x, y) is a point on its graph, the point (-x, -y) will also be on the graph. This is due to the symmetry of odd functions with respect to the origin, complying with their defining property y(x) = -y(-x).
Step-by-step explanation:
If a function is an odd function and (x, y) is a point on its graph, then the point (-x, -y) will also be on the graph. This is because an odd function, as defined by the relationship y(x) = −y(−x), is symmetric with respect to the origin. When a point on the graph of an odd function is reflected about the y-axis and then about the x-axis, the point lands on another valid point on the graph. This means that for every point (x, y) on the graph of an odd function, the point (-x, -y) will also exist on the graph, satisfying the definition of an odd function.
To further clarify, if you take the point (x, y) on an odd function and transform it to (−x, −y), it involves both flipping the x value to its negative, which will flip the point to the other side of the y-axis, and flipping the y value to its negative, which would flip the point across the x-axis. The combined reflections ensure that the resulting point (−x, −y) will still lie on the function's graph.
Therefore, the correct answer to the student's question is option b) (-x, -y).