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 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 negative y right parenthesis is on the graph of 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 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 identify the correct statement regarding the relationship between the points on the graph of \( f(x) \) and \( f(-x) \), we first need to understand the transformation involved when we consider \( f(-x) \).

When we have a point \( (x, y) \) on the graph of \( f(x) \), it means \( y = f(x) \).

For \( f(-x) \), the x-coordinate is negated. Thus, if we plug in \( -x \) into the function, we have:

\[ y' = f(-x) \]

Therefore, if \( (x, y) \) is on the graph of \( f(x) \), the corresponding point on the graph of \( f(-x) \) would be \( (-x, y) \). This describes a reflection over the y-axis.

Thus, the correct statement is:

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

So the correct response is:

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