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Assuming you want the range of
-4cos(2x)
the range of the cosine function is -1 to 1. When that is scaled by a factor of -4, it becomes 4 to -4.
The range of F(x) is [-4, 4] in interval notation.
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If you want the range of
F(x) = -4cos²(x)
that range will be -4×[0, 1] = [-4, 0].
-4cos(2x)
the range of the cosine function is -1 to 1. When that is scaled by a factor of -4, it becomes 4 to -4.
The range of F(x) is [-4, 4] in interval notation.
_____
If you want the range of
F(x) = -4cos²(x)
that range will be -4×[0, 1] = [-4, 0].