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 7 comma 43 right parenthesis

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

(−7,−43)

Answer 1

To find the corresponding point on the graph of \(-f(-x)\) given that the point \((7, 43)\) is on the graph of \(f(x)\), we start with the transformations:

1. The original point \((7, 43)\) tells us that \(f(7) = 43\).
2. When we find \(-f(-x)\), we first need to evaluate \(-f(-x)\) when \(x = -7\) (to correspond with the \(x = 7\) in \(f(x)\)):
   • Thus, we evaluate \(-f(-(-7)) = -f(7)\).
3. Since \(f(7) = 43\), we get:
   • \(-f(7) = -43\).

Now we have evaluated \(-f(-7)\) and found it to be \(-43\). Therefore, the point on the graph of \(-f(-x)\) must be \((-7, -43)\).

The correct response is:

\((-7, -43)\)