Choose the correct statement to describe a true relationship between any point on f(x)

Question

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 x comma negative y right parenthesis is on the graph of f left parenthesis negative 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 negative x comma y right parenthesis is on the graph of f left parenthesis negative x right parenthesis .
If (x,y)
(
𝑥
,
𝑦
)
is on the graph of f(x)
𝑓

Answer 1

To describe the relationship between any point on \( f(x) \) and \( f(-x) \), we can focus on the definition of the function and its transformation.

Let’s analyze the options provided:

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

   • Incorrect: This describes a reflection across the x-axis, which is not what the transformation from \( f(x) \) to \( f(-x) \) does.

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

   • Incorrect: This also suggests a reflection that is not relevant to the transformation we are discussing.

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

   • Correct: This correctly states that reflecting a point over the y-axis results in a point on the graph of \( f(-x) \).

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

   • Correct: This statement is actually a repetition of the previous option (misspelled twice) but it conveys the same true reflection.

Thus, the correct statement to describe the true relationship is:

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