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 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)
.
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)
.

Answer 1

The correct statement that describes the true 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 a point \((x,y)\) is on the graph of a function \(f(x)\), the corresponding point \((x,-y)\) will be on the graph of \(-f(x)\) because the negative of the function simply inverts the \(y\)-coordinate while keeping the \(x\)-coordinate the same.