Graphing a complicated Sine and determining its parts?

Question

Please enlighten me on how to graph this equation, please? and what is the amplitude, period. p. shift, v. shift and range? Thank you so much!

#y=2-sin(-1/2x+pi/4)#

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Answer 1 · 2016-01-20T01:08:52

The vertical shift is upward 2 units ...

factor out the -1/2 ...

#y=2-sin[(-1/2)(x-pi/2)]#

Use the #-1/2# to find the Period ...

Period #=(2pi)/abs(-1/2)=4pi#

Amplitude is the coefficient on #sin# ...

Amplitude #=abs(-1)=1#

Phase Shift #=pi/2# units to the right

Range #=[1,3]#

Here is a sketch ...

Hope that helped

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