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 8 right parenthesis

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

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

(9,8)

Answer 1

To find the vertex of the transformed function \( y = -f(-x) \), starting from the vertex of the original function \( f(x) \) which is given as \( (-9, -8) \), we need to apply the transformations one by one:

1. Horizontal Reflection: The transformation \( f(-x) \) reflects the graph across the y-axis. This will change the x-coordinate of the vertex:

   • Original vertex \( (-9, -8) \) becomes \( (9, -8) \).

2. Vertical Reflection: The transformation \( -f(-x) \) reflects the graph across the x-axis. This will change the y-coordinate of the vertex:

   • So, the vertex \( (9, -8) \) will now become \( (9, 8) \).

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

The correct response is: \[ (9, 8) \]