Choose the correct statement to describe a true relationship between any point on f(x) and −f(x) Responses

Question

If (x,y) is on the graph of f(x), then (x,−y) is on the graph of −f(x).
If (x,y)is on the graph of f(x), then (−x,y) is on the graph of −f(x).
If (x,y) is on the graph of f(x), then (x,y) is on the graph of −f(x).
If left parenthesis x comma y right parenthesis is on the graph line

Answer 1

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

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

This means that for every point \((x,y)\) on the graph of the function \( f(x) \), the corresponding point on the graph of \( -f(x) \) will have the same \( x \)-coordinate and the \( y \)-coordinate will be negated.