How do you graph # y=-1+cos(x-pi)#?

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Answer 1 · 2018-05-28T07:53:47

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First of all, use the fact that the cosine is an even function, i.e. #cos(x)=cos(-x)#. So, #cos(x-pi)=cos(pi-x)#

We also know that #cos(pi-x) = -cos(x)#

The expression becomes #-cos(x)-1#

This means that, starting from #cos(x)#, you apply two transformations:

#cos(x) \to -cos(x) \to -cos(x)-1#

The first transformation is a reflection with respect to the #x# axis, the second is a vertical translation, one unit down.

So, start from the standard cosine function, reflect it and shift it down to get the desired function:

graph{-cos(x)-1}