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

Question

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

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

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

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

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

Answer 1

To find the vertex of the transformed function \( y = -f(-x) \) from the original function with vertex \( (-9, -8) \), we need to analyze the transformations involved:

1. The transformation \( f(-x) \) reflects the graph across the \( y \)-axis. This changes the \( x \)-coordinate of the vertex from \( -9 \) to \( 9 \), while the \( y \)-coordinate remains the same. So, after this transformation, the vertex becomes \( (9, -8) \).

2. The transformation \( -f(x) \) reflects the graph across the \( x \)-axis. This changes the \( y \)-coordinate of the vertex from \( -8 \) to \( 8 \), while the \( x \)-coordinate remains the same. So, after this transformation, the vertex becomes \( (9, 8) \).

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

\[ \text{(9, 8)}. \]

So the correct response is:

(9, 8)