Graph `f(x)= 2cos(x)+2`

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txmedteach | High School Teacher | (Level 3) Associate Educator

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To graph this function, you start with the basic function that the given function is based on: cos(x).

Let's begin by examining how cos(x) looks on the graph:

Let's now double the amplitude, as is called for by the coefficient of 2 for the cosine function: `2cos(x)`. To do this manually, you simply could create the wave by making the peaks reach y=2 instead of y=1, and the troughs reach y=-2 instead of y=-1, as seen here (In red):

Now, we add the last part of the function: the vertical shift of 2. Each y-value on our graph has 2 added to it in the given function, so we simply shift our graph up by 2 (Final answer in blue) (or the axes down by 2, whichever you'd like!):

 

 

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