Question

Choose the statement that best describes a true relationship between any point on f(x)
and −f(−x)
.(1 point)

If (x,y)
is on the graph of f(x)
, then (x,−y)
is on the graph of −f(−x)
.

If (x,y)
is on the graph of f(x)
, then (x,y)
is on the graph of −f(−x)
.

If (x,y)
is on the graph of f(x)
, then (−x,y)
is on the graph of −f(−x)
.

If (x,y)
is on the graph of f(x)
, then (−x,−y)
is on the graph of −f(−x)
.

Answer 1

If (x,y) is on f, then y = f(x). For g(x) = −f(−x) we have g(−x) = −f(−(−x)) = −f(x) = −y, so the point (−x, −y) is on g.

Thus the fourth statement is correct.