Question

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

Answer 1

The correct statement to describe the relationship between any point \((x, y)\) on the graph of \(f(x)\) and 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 means that if you have a point on the graph of the function \(f(x)\), the corresponding point on the graph of \(-f(x)\) will have the same \(x\)-coordinate but the \(y\)-coordinate will be the negative of the original \(y\)-coordinate.