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 negative 7 comma negative 43 right parenthesis

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

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

(−7,43)

Answer 1

To find the point that corresponds to \(-f(-x)\) given the point \((7, 43)\) on the graph of \(f(x)\), we start by analyzing the transformations.

1. The point \((7, 43)\) means \(f(7) = 43\).
2. When we want to find \(-f(-x)\), we first replace \(x\) with \(-x\):
   • This implies that if \(x = 7\), then \(-x = -7\).
3. Next, we evaluate \(f(-7)\). Since we don’t know \(f(-7)\) directly, we take \(x = -7\) to find \(-f(-(-7)) = -f(7)\).
   • Consequently, this leads to \(-f(-7) = -f(7)\).
   • Given that \(f(7) = 43\), we have \(-f(7) = -43\).

So the transformation gives:

\[ (-7, -43) \]

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

The correct answer is:

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