Match the graph of the sine function to the equation over 4

Match the graph of the sine function to the equation over [-4 Pi. 4 Pi]

Solution

here vertical shift is 1/2

from the graph

Amplitude = 3/2

period = =pi

phase shift is = -pi/4/pi= -1/4

so we can write Y = Asin(BX+C) + D

where A= amplitude

period = 2pi/B

phase shift = -C/B

vertical shift (D)=1/2

so y = 3/2sin(1/2 x -pi/4) +1/2

so it is option A

you can find answer in other way also

from the graph take some points

option A is the correct answer

plug x =-pi/4 then we get y=-1 and in the graph also y=-1