Answer:
B. [tex]-2\frac{1}{2} \leq y \leq \frac{1}{2}[/tex]
Step-by-step explanation:
The given trigonometric function is
[tex]f(x)=\frac{3}{2}cos4x-1[/tex].
The amplitude of this function is [tex]\frac{3}{2}[/tex], so under normal circumstances the range is supposed to be
[tex]-\frac{3}{2} \leq y \leq \frac{3}{2}[/tex]
But the [tex]-1[/tex] is a downward vertical shift.
Therefore the normal boundaries of the range will shift down one unit to give the range of the transformed function.
We subtract 1 from the lower boundary to get [tex]-\frac{3}{2}-1=-2\frac{1}{2}[/tex]
We also subtract 1 from the upper boundary to get [tex]-frac{3}{2}-1=\frac{1}{2}[/tex]
Hence the range is
[tex]-2\frac{1}{2} \leq y \leq \frac{1}{2}[/tex]
Also see graph
