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

if the original function has a vertex of (−9,−8)

Responses

(9,−8)

(−9,8)

(−9,−8)

(9,8)

1 answer

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

  1. Horizontal Reflection (f(-x)): Changing \( f(x) \) to \( f(-x) \) reflects the graph across the y-axis. This changes the x-coordinate of the vertex but leaves the y-coordinate the same. If the original vertex is at \((-9, -8)\), reflecting it will give us \((9, -8)\).

  2. Vertical Reflection (-f(-x)): Changing \( f(-x) \) to \(-f(-x)\) reflects the graph across the x-axis. This changes the y-coordinate of the vertex while keeping the x-coordinate the same. So, for our new vertex \((9, -8)\), reflecting it across the x-axis gives us \((9, 8)\).

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

The correct answer is: (9, 8).