Choose the correct statement to describe 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 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 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

To analyze the relationship between a point on the graph of \( f(x) \) and the graph of \( -f(x) \), let's break down the statements.

1. A point \( (x, y) \) on the graph of \( f(x) \) means \( y = f(x) \).
2. For \( -f(x) \), the corresponding point when we negate the function is \( (x, -y) \), which means \( y = -f(x) \).

Thus, if \( (x, y) \) is on the graph of \( f(x) \), then \( (x, -y) \) should be on the graph of \( -f(x) \).

Given this reasoning, the correct statement is:

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