A spring bounces up and down according to the model d (t) = 4sin (30t) + 3 where d (t) is the displacement in cm from the rest position and t is time in seconds. What is the range?

The range of d (t) is [-1, 7]

Step-by-step explanation:

The range of d (t) can be found with the lowest and the highest value of the function.

The highest value of d (t) occurs when the sine function is equal to 1 (because the value multiplying the sine is a positive value), and the lowest function occurs when it is equal to - 1.

So we have that:

d_max = 4*1 + 3 = 7

d_min = 4 * (-1) + 3 = - 1

So the range of d (t) is [-1, 7].