Question

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

If (x,y)
(
𝑥
,
𝑦
)
is on the graph of f(x)
𝑓
(
𝑥
)
, then (−x,y)
(
−
𝑥
,
𝑦
)
is on the graph of −f(x)
−
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 x right parenthesis .

If (x,y)
(
𝑥
,
𝑦
)
is on the graph of f(x)
𝑓
(
𝑥
)
, then (x,−y)
(
𝑥
,
−
𝑦
)
is on the graph of −f(x)
−
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)
(
𝑥
,
𝑦
)
is on the graph of f(x)

Answer 1

The correct statement to describe 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 means that for every point \((x, y)\) on the graph of the function \( f(x) \), the corresponding point \((x, -y)\) will be on the graph of the function \( -f(x) \). This indicates a reflection over the x-axis.