Choose the correct statement to describe a true relationship between any point on f(x) and −f(x) .(1 point)

Question

Responses

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 of f left parenthesis x right parenthesis , then left parenthesis x comma negative y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .

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 of f left parenthesis x right parenthesis , then left parenthesis negative x comma y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .

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 of f left parenthesis x right parenthesis , then left parenthesis negative x comma negative y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .

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 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 if you have a point \((x, y)\) on the graph of the function \( f(x) \), then the point will reflect across the x-axis to give you the point \((x, -y)\) on the graph of \( -f(x) \).