Find the range of y = 3/2 cos 4x - 1i tried it and i got an answer of -1/2 < = y < = 3/ but this is not one of the choices! choices: a) -1/2 < = y < = 1/2b) -2 1/2 < = y < = 1/2c) -3/2 < = y < =3/2d) -5 < = y < =3

B.

Step-by-step explanation:

The given trigonometric function is

.

The amplitude of this function is , so under normal circumstances the range is supposed to be

But the 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

We also subtract 1 from the upper boundary to get

Hence the range is

Also see graph

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: