The correct statement that best describes the relationship between any point on \( f(x) \) and \( -f(-x) \) is:
If \((x,y)\) is on the graph of \( f(x) \), then \((-x,-y)\) is on the graph of \( -f(-x) \).
This is because if \((x, y)\) is a point on \( f(x) \), that means \( f(x) = y \). To find the relationship with \( -f(-x) \), we evaluate it:
- The transformation to \( -f(-x) \) reflects the function across the \( y \)-axis and then reflects it again across the \( x \)-axis.
- Thus, \((-x)\) will yield \( -f(-x) \), which will be \(-y\).
Therefore, the point \((-x, -y)\) will indeed lie on the graph of \( -f(-x) \).