Ask a New Question
Menu

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

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 negative 9 comma 8 right parenthesis

(9,8)

1 answer

To find the vertex of \( y = -f(-x) \) when the original function \( f(x) \) has a vertex of \( (-9, -8) \), we should first consider the transformations involved.

  1. Reflection over the x-axis: The negative sign in front of \( f \) indicates that the graph is reflected over the x-axis. This changes the y-coordinate of the vertex from \( -8 \) to \( 8 \).

  2. Reflection over the y-axis: The transformation \( f(-x) \) reflects the graph over the y-axis. This changes the x-coordinate of the vertex from \( -9 \) to \( 9 \).

Therefore, applying both transformations, the new vertex becomes \( (9, 8) \).

Thus, the vertex of \( y = -f(-x) \) is:

\((9, 8)\)