Question

If the point (13,−7) ( 13 , − 7 ) is on the graph of f(x) 𝑓 ( 𝑥 ) , what point must be on the graph of f(−x) 𝑓 ( − 𝑥 ) ?(1 point) Responses The point (−13,−7) ( − 13 , − 7 ) must be on the graph of f(−x) 𝑓 ( − 𝑥 ) . The point left parenthesis negative 13 comma negative 7 right parenthesis must be on the graph of f left parenthesis negative x right parenthesis . The point (13,7) ( 13 , 7 ) must be on the graph of f(−x) 𝑓 ( − 𝑥 ) . The point left parenthesis 13 comma 7 right parenthesis must be on the graph of f left parenthesis negative x right parenthesis . The point (13,−7) ( 13 , − 7 ) must be on the graph of f(−x) 𝑓 ( − 𝑥 ) . The point left parenthesis 13 comma negative 7 right parenthesis must be on the graph of f left parenthesis negative x right parenthesis . The point (−13,7) ( − 13 , 7 ) must be on the graph of f(−x) 𝑓 ( − 𝑥 ) .

Answer 1

If the point \((13, -7)\) is on the graph of \(f(x)\), this means that \(f(13) = -7\).

To find the corresponding point on the graph of \(f(-x)\), we substitute \(-x\) into \(f(x)\). Specifically, if we want to find \(f(-13)\):

1. Since we know that \(f(13) = -7\), then to find \(f(-13)\), we can use the relationship of the function reflected over the y-axis.
2. We find that \(f(-x)\) will give us the same output, meaning \(f(-13) = -f(13)\).

However, without specific information about whether \(f(x)\) is even or odd, we simply know that \(f\) at the negative input yields the same output value as at the positive input given the information we have.

Thus, the answer must reflect that if \(f(13) = -7\), then \(f(-13)\) is determined purely by the reflection in the context provided.

Therefore, the correct choice is:

The point \((-13, -7)\) must be on the graph of \(f(-x)\).