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 negative 9 comma negative 8 right parenthesis

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

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

(9,8)

Answer 1

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

1. Horizontal Reflection: The term \( -x \) reflects the graph across the y-axis. If the original vertex is \( (-9, -8) \), applying \( -x \) changes the x-coordinate:

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

2. Vertical Reflection: The term \( -f(x) \) reflects the graph across the x-axis. Hence, this changes the y-coordinate of the new vertex:

   • After the reflection: \( (9, 8) \)

Therefore, the new vertex after applying the transformation \( y = -f(-x) \) is \( (9, 8) \).

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