To analyze the relationship between points on \( f(x) \) and \( -f(-x) \), we start by examining the definitions and transformations involved.
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If \((x, y)\) is a point on the graph of \( f(x) \), then we have: \[ y = f(x) \] This means that \( y \) is equal to \( f(x) \).
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When we evaluate \( -f(-x) \), we need to substitute \(-x\) into the function \( f \), which then gives us: \[ -f(-x) \] Hence, the point corresponding to \(-x\) would be: \[ \text{At } x = -x, \quad y = -f(-x) \]
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Therefore, we want to find the relationship between the points. For the point \((x, y)\), since \( y = f(x) \), we need to consider the substituted values:
- The corresponding point for \(-x\) in \( f \) is \( f(-x) \), which translates to \((−x, f(-x))\).
- To change that value according to the transformation for \(-f(-x)\), we find \( (−x, -f(-x)) \) because of the negative sign.
Given this, the final relationship we can deduce is: If \((x, y)\) is on the graph of \( f(x) \), then we find that for \(-f(-x)\), the point will be: \[ (-x, -y) \]
Thus, the statement that best describes this relationship is: If \((x,y)\) is on the graph of \( f(x) \), then \((-x,-y)\) is on the graph of \(-f(-x)\).