Ask a New Question
Menu

Question

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 8 right parenthesis

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

(9,−8)

1 answer

To determine the vertex of the transformed function \( y = -f(-x) \), we need to understand how the transformations affect the coordinates of the original vertex.

Given the original vertex \( (-9, -8) \):

  1. Reflection over the Y-axis: \( f(-x) \) reflects the graph across the y-axis. This changes the x-coordinate of the vertex from -9 to 9, while the y-coordinate remains the same. This gives us the new vertex: \[ (9, -8) \]

  2. Reflection over the X-axis: The negative sign in front of \( f(-x) \) means we reflect the graph across the x-axis. This changes the y-coordinate from -8 to 8 while the x-coordinate remains 9. This gives us the final vertex: \[ (9, 8) \]

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

So the correct response is: \[ (9, 8) \]