How do you graph #y = -2 - cos(x-pi)#?
1 Answer
This function has the same graph of
Explanation:
When you must graph a composed function, the idea is to recognize every step, and understand the way it affect the graph of a function. So, let's start from the fundamental function
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#cos(x) -> cos(x-pi)# . A change of this kind,#f(x)->f(x+k)# means to translate the graph of the function horizontally. If#k# is positive, we shift to the left, otherwise we shift to the right. Since in your case#k=-pi# , we shift the graph to the left. Note: for this change, you could also have used the identity#cos(x-pi)=-cos(x)# , and observe that#f(x)-> -f(x)# consists in a horizontal flip (symmetry with respect to the#x# -axis. -
Now we have to change sign again. Since we just noted that
#cos(x-pi)=-cos(x)# , then#-cos(x-pi)=-(-cos(x))=cos(x)# . So, you can rewrite your function as#cos(x)-2# , making it much easier. -
So, the last step to consider is
#cos(x)->cos(x)-2# . A change of this kind,#f(x)->f(x)+k# means to translate the graph of the function vertically. If#k# is positive, we shift upwards, otherwise we shift downwards. Since in your case#k=-2# , we shift the graph downwards.
