To understand how the graph of \( f(-x) \) relates to the graph of \( f(x) \), we can analyze the transformation involved.
The point \( (13, -7) \) means that \( f(13) = -7 \). When we consider \( f(-x) \), we need to replace \( x \) with its negative counterpart.
For the x-coordinate of the original point \( (13, -7) \):
- The input \( x = 13 \) in \( f(x) \) becomes \( x = -13 \) in \( f(-x) \).
The output \( f(-x) \) will therefore be \( f(-(-13)) = f(13) \).
Since we established that \( f(13) = -7 \), we now have:
- For \( x = -13 \) in \( f(-x) \), the corresponding output is \( f(-13) = -7 \).
Thus, the point \( (-13, -7) \) must be on the graph of \( f(-x) \).
So, the correct response is:
The point (−13,−7) must be on the graph of f(−x).