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 8 right parenthesis

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

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

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

Answer 1

To find the vertex of the function \(y = -f(-x)\), we need to analyze the transformations applied to the original vertex.

Given that the original function \(f(x)\) has a vertex at \((-9, -8)\):

1. The transformation \(f(-x)\) reflects the function across the y-axis. This changes the x-coordinate of the vertex from \(-9\) to \(9\), so the new vertex is \((9, -8)\).

2. The negative sign in front, \(-f(-x)\), reflects the function across the x-axis. This changes the y-coordinate of the vertex from \(-8\) to \(8\), so now the vertex becomes \((9, 8)\).

Therefore, the vertex of \(y = -f(-x)\) is \((9, 8)\).

Thus, the correct response is:

(9, 8).