The statement that best describes the true relationship between any point on \( f(x) \) and \( -f(-x) \) is:
If (x, y) is on f(x), then (-x, -y) is on -f(-x).
This is because when you take the function \( f(x) \), the point \( (x, y) \) corresponds to \( f(x) = y \). When you evaluate \( -f(-x) \), you first find \( f(-x) \) which would give you some value (let's call it \( y' \)), and then you take the negative of that, resulting in \( -y' \).
Furthermore, since \( f(-x) \) represents the function reflected across the y-axis, and then negating this function reflects it across the x-axis, this leads to the conclusion that the point corresponding to \( (x, y) \) on \( f(x) \) becomes \( (-x, -y) \) on \( -f(-x) \).
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