If the point (7,43)

Question

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

(7,−43)
left parenthesis 7 comma negative 43 right parenthesis

(−7,−43)
left parenthesis negative 7 comma negative 43 right parenthesis

(−7,43)
left parenthesis negative 7 comma 43 right parenthesis

(7,43)

Answer 1

If the point (7, 43) is on the graph of \( f(x) \), it means \( f(7) = 43 \).

To find the corresponding point on the graph of \( -f(-x) \), we follow these steps:

1. Substitute \( -x \): For \( x = 7 \), we get \( -x = -7 \).

2. Find \( f(-7) \): Since we don't directly have it from the point given, we can figure it out as follows:

   • Since \( f(7) = 43 \), we need to evaluate \( -f(-7) \). But we also need \( f(-7) \) explicitly.

3. We know that if \( -f(-x) \) takes \( x = -7 \), we have:

   \[ -f(-(-7)) = -f(7) = -43 \]

Thus, the point that corresponds to \( (7, 43) \) on the graph of \( -f(-x) \) is \( (-7, -43) \).

Therefore, the answer is:

\[ \boxed{(-7, -43)} \]