If you are given f(x)

, what is the difference between the reflections −f(x)
and f(−x)
?(1 point)
Responses

There is no difference in these reflections. Both reflections would have the same graph.
There is no difference in these reflections. Both reflections would have the same graph.

The reflection −f(x)
moves the graph up 1 unit, while the reflection f(−x)
moves the graph down 1 unit.
The reflection negative f times x moves the graph up 1 unit, while the reflection f of negative x moves the graph down 1 unit.

−f(x)
is a reflection over the x-axis, where the y-values become their opposites. f(−x)
is a reflection over the y-axis, where the x-values become their opposites.
negative f times x is a reflection over the x-axis, where the y-values become their opposites. f of negative x is a reflection over the y-axis, where the x-values become their opposites.

−f(x)
is a reflection over the y-axis, where the x-values become their opposites. f(−x)
is a reflection over the x-axis, where the y-values become their opposites.

1 answer

The correct response is:

−f(x) is a reflection over the x-axis, where the y-values become their opposites. f(−x) is a reflection over the y-axis, where the x-values become their opposites.

To clarify:

  • −f(x) flips the graph of the function across the x-axis.
  • f(−x) flips the graph of the function across the y-axis.