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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

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 class=

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ANSWER

E.

[tex]y = 2 \sin( \theta) - 3[/tex]

EXPLANATION

The parent function

[tex]y = \sin( \theta) [/tex]

can be shifted down by 3 units to obtain

[tex]y = \sin( \theta) - 3[/tex]

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

[tex]y = 2 \sin( \theta) [/tex]

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

[tex]y = 2\sin( \theta) - 3[/tex]

The correct choice is E.

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