SOLUTION: https://gyazo.com/6cca872e14f76df34ecefd2f460c3032

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Question 1179769: https://gyazo.com/6cca872e14f76df34ecefd2f460c3032
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
parent function:+f%28x%29+=+sin%28x%29
Periodicity of sin (x ) is+2pi+.
+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+sin%28x%29%29+
This is the general equation for a sinusoidal function:
f%28x%29+=+a+sin+%28k%28x-d%29%29+%2B+c
a determines amplitude:
a+%3E+1 or+a+%3C+-1 → vertical stretch
-1+%3C+a+%3C+1 → vertical compression
a+%3C+0→ reflection in x-axis

k determines period:
k+%3E1 or k+%3C+-1 → horizontal compression by 1%2Fk
-1+%3C+k+%3C+1 → horizontal stretch by 1%2Fk
k+%3C+0 → reflection in y-axis
d determines phase shift:
d+%3E+0→ shift to the right "d" units.
d+=+0 → no phase shift
d+%3C+0→ shift to the left "d" units
c determines vertical shift:
c+%3E+0 → shift up "c" units
c+=+0 → no vertical shift
c+%3C+0→ shift down "c" units
you are given:
f%28x%29+=+3sin+%282%28x-pi%2F6%29%29+%2B+1
so, in this case
periodicity is+2pi%2Fk=2pi%2F2=pi+
a=3=>+a+%3E+1+ → vertical stretch
k=2=> k+%3E1 → horizontal compression by 1%2Fk=1%2F2
d=pi%2F6=> d+%3E+0 → shift to the right "pi%2F6" units
c=1=> c+%3E+0→ shift up "1" unit