Question

If the point (13,−7)
(
13
,
−
7
)
is on the graph of f(x)
𝑓
(
𝑥
)
, what point must be on the graph of f(−x)
𝑓
(
−
𝑥
)
?(1 point)
Responses

The point (13,−7)
(
13
,
−
7
)
must be on the graph of f(−x)
𝑓
(
−
𝑥
)
.
The point left parenthesis 13 comma negative 7 right parenthesis must be on the graph of f left parenthesis negative x right parenthesis .

The point (−13,−7)
(
−
13
,
−
7
)
must be on the graph of f(−x)
𝑓
(
−
𝑥
)
.
The point left parenthesis negative 13 comma negative 7 right parenthesis must be on the graph of f left parenthesis negative x right parenthesis .

The point (−13,7)
(
−
13
,
7
)
must be on the graph of f(−x)
𝑓
(
−
𝑥
)
.
The point left parenthesis negative 13 comma 7 right parenthesis must be on the graph of f left parenthesis negative x right parenthesis .

The point (13,7)
(
13
,
7
)
must be on the graph of f(−x)
𝑓
(
−
𝑥
)
.

Answer 1

Given that the point \((13, -7)\) is on the graph of \(f(x)\), this means that \(f(13) = -7\).

To find the point on the graph of \(f(-x)\), we need to substitute \(-x\) in place of \(x\) in the function. Specifically, we want to evaluate \(f(-x)\).

If \(x = 13\), then \(-x = -13\). Thus, we can determine:

\[
f(-13) = f(-x) \text{ when } x = 13
\]

Since \(f(13) = -7\), then by the property of the function:

\[
f(-13) = -7
\]

This means the point \((-13, -7)\) is on the graph of \(f(-x)\).

Therefore, the correct response is:

**The point \((-13, -7)\) must be on the graph of \(f(-x)\).**