Which of the following is the vertex of y=−f(−x)

Question

if the original function has a vertex of (−9,−8)
?(1 point)
Responses

(−9,−8)
left parenthesis negative 9 comma negative 8 right parenthesis

(9,−8)
left parenthesis 9 comma negative 8 right parenthesis

(9,8)
left parenthesis 9 comma 8 right parenthesis

(−9,8)

Answer 1

To find the vertex of the function \( y = -f(-x) \) given that the original function \( f(x) \) has a vertex of \((-9, -8)\), we need to consider how the transformations affect the vertex.

1. Horizontal Reflection and Translation: The transformation \( f(-x) \) reflects the graph of the function across the y-axis. Thus, the x-coordinate of the vertex changes sign:

   • The x-coordinate of the original vertex \(-9\) becomes \(9\).
   • The y-coordinate remains the same: \(-8\).

   So, after this transformation, the new vertex is \((9, -8)\).

2. Vertical Reflection: The transformation \( -f(-x) \) then reflects the graph across the x-axis. This changes the sign of the y-coordinate:

   • The x-coordinate remains \(9\).
   • The y-coordinate \(-8\) becomes \(8\).

   Thus, the final vertex after both transformations is \((9, 8)\).

Based on this analysis, the correct answer is:

\((9, 8)\)