If the point (7,43)

Question

(
7
,
43
)
is on the graph of f(x)
𝑓
(
𝑥
)
, what point must be on the graph of −f(−x)
−
𝑓
(
−
𝑥
)
?(1 point)
Responses

(7,43)
(
7
,
43
)
left parenthesis 7 comma 43 right parenthesis

(−7,43)
(
−
7
,
43
)
left parenthesis negative 7 comma 43 right parenthesis

(7,−43)
(
7
,
−
43
)
left parenthesis 7 comma negative 43 right parenthesis

(−7,−43)

Answer 1

To find the point that must be on the graph of \(-f(-x)\) given that the point \((7, 43)\) is on the graph of \(f(x)\), we need to perform two transformations:

1. Horizontal reflection: The first transformation \(f(-x)\) reflects the graph across the y-axis. Thus, the point \((7, 43)\) becomes \((-7, 43)\).

2. Vertical reflection: The second transformation \(-f(-x)\) reflects the graph across the x-axis. Thus, the point \((-7, 43)\) becomes \((-7, -43)\).

Combining these two transformations, the point \((7, 43)\) results in the point \((-7, -43)\) on the graph of \(-f(-x)\).

Therefore, the point that must be on the graph of \(-f(-x)\) is \((-7, -43)\).