Question

If the point (7,43) 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 43 right parenthesis (−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 negative 7 comma 43 right parenthesis

Answer 1

To find the point that must be on the graph of \(-f(-x)\), we start with the given point on the graph of \(f(x)\):

1. The point \((7, 43)\) indicates that \(f(7) = 43\).

Next, we need to determine the value of \(-f(-x)\):

2. To find the corresponding point on the graph of \(-f(-x)\), we can start by evaluating \(-f(-x)\) at \(x = -7\):

   • First, calculate \(f(-7)\). Since we don't have \(f(-7)\) directly, we will use the known value \(f(7)\).
   • We do not have information about \(f(-7)\) directly, but for the sake of transformation, we'll treat it as \(f(-7) = k\) for some value \(k\).

3. Now, substituting into \(-f(-x)\):

   • \(-f(-(-7)) = -f(7)\).
   • Since \(f(7) = 43\), we have \(-f(7) = -43\).

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

Therefore, the correct answer is:

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