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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)?

1. (-9, -8)
2. (9, -8)
3. (9,8)
4. (-9, 8)

1 answer

To determine the vertex of \( y = -f(-x) \) given that the original function has a vertex at \((-9, -8)\), we must first note how transformations affect the vertex.

  1. Horizontal Reflection - The \( -x \) inside the function indicates a reflection across the y-axis. This will change the x-coordinate of the vertex from \(-9\) to \(9\).

  2. Vertical Reflection - The \( -f(x) \) indicates a reflection across the x-axis. This will change the y-coordinate of the vertex from \(-8\) to \(8\).

Thus, the transformations lead us to:

  • The x-coordinate becomes \(9\) (from \(-9\) to \(9\)).
  • The y-coordinate becomes \(8\) (from \(-8\) to \(8\)).

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

The correct answer is 3. (9, 8).