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 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 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 negative 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)
.

Answer 1

The correct statement that best describes 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 is because:

1. If \( (x, y) \) is on the graph of \( f(x) \), then \( y = f(x) \).
2. To find the corresponding point on \( -f(-x) \), you substitute \( -x \) into \( f(x) \), giving \( -f(-x) \).
3. That means you'd evaluate \( -f(-x) \), leading to the point \( (-x, -y) \) since \( y = f(x) \) transforms to \( -y = -f(-x) \).

So, the transformation of the graph reflects over the \( y \)-axis (due to the \( -x \)) and then reflects over the \( x \)-axis (due to the negative sign in front).