To analyze the statement involving a point on the graph of \( f(x) \) and its relation to \( -f(-x) \), we start by noting that if \( (x, y) \) is a point on the graph of \( f(x) \), this means:
\[ f(x) = y \]
We want to look at the point \( -f(-x) \). To find the \( y \)-coordinate of this point, we first evaluate \( -f(-x) \):
- Substitute \( -x \) into \( f(x) \): If \( (x, y) \) is on \( f(x) \), then \( f(-x) \) gives us the value when the input is \( -x \).
- The \( y \)-coordinate for the point corresponding to \( -f(-x) \) would thus be: \[ -f(-x) \]
Now considering the transformations:
- \( f(-x) \) reflects the graph of \( f(x) \) over the y-axis.
- \( -f(-x) \) reflects that result over the x-axis.
Thus, if \( (x, y) \) is a point on the graph of \( f(x) \), we have the following final relationship based on the transformations applied:
- The transformation gives us \( (-x, -y) \) on the graph of \( -f(-x) \).
Therefore, the statement that best describes the relationship is:
If \((x, y)\) is on the graph of \( f(x) \), then \((-x, -y)\) is on the graph of \( -f(-x) \).