For any function in general, where y= a \cdot f( b (x-c) ) + d, to graph it we work from the inside out.
So first graph f(x) as normal. Then move that graph c units to the right. If it is (x+c) instead, then c units to the left.
Then squeeze the shifted graph by a factor of b times horizontally. If like in this case, its less than 1, write it in the form 1/b (b is 2 for your example). For when its in the form 1/b,
then stretch it by a factor of b times horizontally.
Then stretch the whole thing vertically by a factor of a. If a is negative, also flip the graph upside down. Similar thing, if a is less than one, rewrite the coefficient as 1/a. Then squeeze vertically by a factor of a.
Now just must that up by d units, or if d is negative, down d units.
Its really must easier to put into practice and to understand than it looks.
For this one, get the normal Cosine graph, stretch it horizontally by a factor of 2. Eg where the normal cosine graph first intercepts the x-axis at pi/2, it is now at pi.
Then, stretch it up and down by a factor of 2. So all the points that it is 0 stay the same, where they are 1 they becoming 2, and where they were -1 they become -2.
Now just shift that down by -2. So where they were -2, it becomes -4, and where they were 2, it becomes 0.
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