Question

Find the range of y = 3/2 cos 4x - 1

Answer 1

Answer:

B. $-2\frac{1}{2} \leq y \leq \frac{1}{2}$

Step-by-step explanation:

The given trigonometric function is

$f(x)=\frac{3}{2}cos4x-1$.

The amplitude of this function is $\frac{3}{2}$, so under normal circumstances the range is supposed to be

$-\frac{3}{2} \leq y \leq \frac{3}{2}$

But the $-1$ 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 $-\frac{3}{2}-1=-2\frac{1}{2}$

We also subtract 1 from the upper boundary to get $-frac{3}{2}-1=\frac{1}{2}$

Hence the range is

$-2\frac{1}{2} \leq y \leq \frac{1}{2}$

Also see graph