To analyze the relationship between any point on \( f(x) \) and \( -f(-x) \), let’s start by understanding what the transformation entails.
- If \( (x, y) \) is a point on the graph of \( f(x) \), it means \( y = f(x) \).
- When we consider \( -f(-x) \), we first apply the transformation \( -x \), which reflects the point across the y-axis. This transforms the point to \( (-x, f(-x)) \).
- Then, we apply the negative, leading to \( -f(-x) \), which gives us \( (-x, -f(-x)) \).
Thus, if we start with the point \( (x, y) \) from \(f(x)\), it transforms to \( (-x, -y) \) on the graph of \( -f(-x) \).
Therefore, the statement that best describes a true 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 \( -f(-x) \).