Find the range of y = 3cos4x - 2.-5 ≤ y ≤ 51 ≤ y ≤ 3-3 ≤ y ≤ 3-5 ≤ y ≤ 1

To find the range of the function y = 3cos(4x) - 2, we need to determine the minimum and maximum values that y can take.

Step 1: Find the maximum value of y: The maximum value of the cosine function is 1. Therefore, the maximum value of 3cos(4x) is 3. When we subtract 2 from this, we get a maximum value of y = 3 - 2 = 1.

Step 2: Find the minimum value of y: The minimum value of the cosine function is -1. Therefore, the minimum value of 3cos(4x) is 3(-1) = -3. When we subtract 2 from this, we get a minimum value of y = -3 - 2 = -5.

Therefore, the range of the function y = 3cos(4x) - 2 is -5 ≤ y ≤ 1.