How do you graph #f(x)= 2+csc(2x+2)#?

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Answer 1 · 2017-12-10T11:36:23

As shown below:

The first thing we must consider is the transformations that #csc x # must undergo to reach #2+ csc(2x+2 )#

So first it must be translated by #(0,2)# or in other words, shifted upward by 2 units: yielding # 2+ cscx #

Then stretched by a scale factor of #1/2# in the #x# direction:
yielding #2+csc(2x) #

Then translate by the vector #(-1,0)# to yield: #2+csc(2(x+1)) #
#= 2+ csc(2x+2) #

#=> #

#cscx: # graph{cscx [-10, 10, -5, 5]}

#2+cscx #: graph{cscx + 2 [-9.71, 10.29, -2.32, 7.68]}

#2+csc2x # : graph{2+ csc(2x) [-9.71, 10.29, -2.32, 7.68]}

#2+csc(2x+2) #: graph{2+csc(2x+2) [-9.71, 10.29, -2.32, 7.68]}