Determine the equation from the graph says the problem but i dont know how to do this, i saw my notes but still confuse me : (

y = 2·sec((x -3π/2)/2) -4

The general shape of the curve suggests the parent function is a secant or cosecant function. Here, we choose to use the secant. It might help to familiarize yourself with the graph of a secant function (shown in the second attachment).

The centerline between the local maximum and local minimum is at -4, so that is the vertical offset.

The distance between that centerline and a local maximum or minimum is 2 units, so the vertical expansion factor is 2.

The horizontal distance between the local maximum and local minimum is 2π, so represents a horizontal expansion by a factor of 2.

The location of the local minimum is at x=3π/2, so that represents the horizontal offset.

The form of the function with these various transformations is ...

... g(x) = (vertical scale factor) × f((x - (horizontal offset))/(horizontal expansion factor)) - (vertical offset)

Filling in the function and the various values, we get ...

... y = 2·sec((x -3π/2)/2) -4