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

Answer 1

To find the vertex of the transformed function \(y = -f(-x)\) given the vertex of the original function \(f(x)\) is \((-9, -8)\), we need to analyze the transformations step by step.

1. **Horizontal Reflection (f(-x))**: The reflection across the y-axis changes the x-coordinate of the vertex:
- Original vertex: \((-9, -8)\)
- After reflection: \((9, -8)\)

2. **Vertical Reflection (-f(-x))**: The reflection across the x-axis changes the y-coordinate of the vertex:
- After vertical reflection: \((9, 8)\)

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

The correct response is \((9, 8)\).