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 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).
1 answer
The correct statement to describe the relationship between points 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 \( -f(x) \).
So the first option is correct. This is because the transformation from \( f(x) \) to \( -f(x) \) reflects the graph across the x-axis, changing the sign of the y-coordinate.
