How do you graph #y=5+sin(1/2x)#?

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Answer 1 · 2018-06-07T22:49:19

The graph will be a sine function centered on #y =5# with a period of #4pi#

#y=5+sin(1/2x)#

#y=sin(1/2x) +5#

Standard Form is:

y=asin(bx-c) + d

a=amplitude or vertical stretch/compression
b=horizontal stretch/compression
c=horizontal shift
d=vertical shift

Your function #b=1/2# and #d=5#:

a horizontal stretch by a factor of 2 will make the period #4pi#.

a vertical shift up 5 units.

The graph will be a sine function centered on #y =5# with a period of #4pi#

graph{sin(1/2x) +5 [-11.58, 8.42, 0.68, 10.68]}