Graphing a complicated Sine and determining its parts?

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)#

1 Answer
Jan 20, 2016

The vertical shift is upward 2 units ...

Explanation:

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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