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

Question

𝑦
=
−
𝑓
(
−
𝑥
)
if the original function has a vertex of (−9,−8)
(
−
9
,
−
8
)
?(1 point)
Responses

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

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

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

(9,−8)

Answer 1

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

1. Reflection Across the Y-axis: The transformation \( f(-x) \) reflects the graph of \( f(x) \) across the y-axis. This means that the x-coordinate of the vertex will change sign. Given the original vertex of \( (-9, -8) \), the x-coordinate becomes \( 9 \), while the y-coordinate remains the same for now:

   Original vertex: \( (-9, -8) \) → After reflection: \( (9, -8) \).

2. Reflection Across the X-axis: The transformation \( -f(-x) \) then reflects the graph across the x-axis. This means that the y-coordinate will change sign. So now we take our vertex from the previous step \( (9, -8) \) and reflect it across the x-axis:

   After reflection: \( (9, 8) \).

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

The answer is:

\( (9, 8) \).