To choose the correct statement that describes the relationship between any point on \( f(x) \) and \( f(-x) \), we consider what it means for a function \( f(x) \).
Given a point \( (x, y) \) on the graph of \( f(x) \), we have:
- \( f(x) = y \)
Now, for \( f(-x) \), it means we are essentially evaluating the function at the opposite input:
- \( f(-x) \)
The relationship between the points can be described as follows:
- If \( (x, y) \) is on the graph of \( f(x) \), then the corresponding point \( (-x, f(-x)) \) is on the graph of \( f(-x) \).
The correct choice from the given options is:
If (x,y) is on the graph of f(x) then (−x,y) is on the graph of f(−x).
This statement reflects the fact that \( f(-x) \) outputs the same \( y \)-value for the input \( -x \) compared to the \( x \)-value on the original function \( f(x) \).
Thus, the correct response from the options provided is:
If (x,y) is on the graph of f(x), then (−x,y) is on the graph of f(−x).