Create the sin curve graph of y=3sin(x-pi)+1

Question

jdoe0001 · Answer

do you know the graph for sin(x)?

jdoe0001 · Answer

y= 3                     sin(x          -pi      )                                     +1
      ^                                           ^                                               ^
   amplitude                     horizontal shift                       vertical shift

psymon · Answer

period of sinx = 2pi (the graph copies itself and goes through a full cyvle every 2 pi)

Asin(bx - c) A is the amplitude. The normal range of sinx is [-1, 1]. The amplitude multiplies these endpoints to give you your new range. Basically, 3 is your amplitude, so your range now goes from [-3. 3]. 

-c is your phase shift, how much your graph moves left or right. When you have (bx-c), your graph moves right c units. When you have (bx+c), your graph moves left c units.

And finally, the + 1 tacked up shifts your entire graph up one unit. So that being said, the range we mentioned before of [-3, 3] goes up 1 and becomes [-2, 4]. And then yeah, the rest of it is knowing what the original sin graph looks like and applying those changes:

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