Amplitude of 16 units, a period of 5 units, a vertical displacement of 3 units up and a phase shift of 2.5 units left.

The question is incomplete. The complete question is :

A sine function that has an amplitude of 16 units, a period of 5 units,a vertical displacement of 3 units up and a phase shift of 2.5 units left. Graph this function and show each step.

Solution :

The standard form of the sine function is

y = a sin (bx - c) + d

Here given :

Amplitude, a = 16

Period :  

            ⇒

Phase shift :  

                  ∴

The vertical displacement : d = 3 units up

Now substituting a, b, c and d values in the standard form gives :

The graph is attached below.