y = 4 sin [ ( pi/ 4)x - pi/2 ] - 3
Look at the graph here : https://www.desmos.com/calculator/qrjaot4u81
The rate of change will be positive from 2 < x < 4 and then on every interval given by
( 8x , 8x + 4)
where x is a natural number
The rate of change will be negative from 4 < x < 8 and then on every interval given by
( 8x + 4, 8x + 8)
where x is a natural number
The rate of change will be 0 at every 4x where x is a natural number