Choose the correct statement to describe a true relationship between any point of f (x) and f (-x).

Question

1. If (x, y) is on the graph lf f (x) then (-x, -y) is on the graph of f (-x)
2. If (x, y) is on the graph lf f (x) then (x, y) is on the raph of f (-x)
3. If (x, y) is on the graph of f (x), then (-x, y) is on the graph of f (-x)
4. If (x, y) is on the graph of f (x) then (x, -y) is on the graph of f (-x)

Answer 1

The correct statement to describe the relationship between any point of \( f(x) \) and \( f(-x) \) is:

3. If (x, y) is on the graph of \( f(x) \), then (-x, y) is on the graph of \( f(-x) \).

This is because the function \( f(-x) \) takes the input \(-x\) and outputs the same value as \( f(x) \) does for that specific input. Hence, for a point \((x, y)\) on \( f(x) \), where \( y = f(x) \), it follows that \((-x, f(-x)) = (-x, y)\) will be on the graph of \( f(-x) \).