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 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)
.
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)
.

Answer 1

To analyze the relationship between any point on \( f(x) \) and \( -f(-x) \), let’s start by understanding what the transformation entails.

1. If \( (x, y) \) is a point on the graph of \( f(x) \), it means \( y = f(x) \).
2. When we consider \( -f(-x) \), we first apply the transformation \( -x \), which reflects the point across the y-axis. This transforms the point to \( (-x, f(-x)) \).
3. Then, we apply the negative, leading to \( -f(-x) \), which gives us \( (-x, -f(-x)) \).

Thus, if we start with the point \( (x, y) \) from \(f(x)\), it transforms to \( (-x, -y) \) on the graph of \( -f(-x) \).

Therefore, the statement that best describes a 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 \( -f(-x) \).