Question

Which of the following equations of y = sin x has been transformed by a vertical shift down 3 units and stretch factor of 2?

A. y = sin 20
B. y = 2 sin +3
C. y = -2sin 8 - 3
D. y = 3 sin 0 - 2
E. y = 2sin 0-3

Answer 1

E.

`y = 2 \sin( \theta) - 3`

Step-by-step explanation

The parent function

`y = \sin( \theta)`

can be shifted down by 3 units to obtain

`y = \sin( \theta) - 3`

Also, when the basic sine function is stretched vertically by a factor of 2, the equation becomes,

`y = 2 \sin( \theta)`

Therefore, a vertical shift down 3 units and stretch factor of 2 gives the equation:

`y = 2\sin( \theta) - 3`

The correct choice is E.