Choose the statement that best describes a true relationship between any point on f(x)

Question

and −f(−x)
.(1 point)
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 y right parenthesis is on the graph of negative f left parenthesis negative 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 negative y right parenthesis is on the graph of negative f left parenthesis negative 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 negative 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 that describes the relationship between a point \((x, y)\) on the graph of \(f(x)\) and the point on the graph of \(-f(-x)\) is:

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

This is because the transformation from \(f(x)\) to \(-f(-x)\) involves reflecting the graph over the y-axis (changing \(x\) to \(-x\)) and then reflecting it over the x-axis (changing \(y\) to \(-y\)).