Question

Help !

Answer 1

the graph is cyclical which indicates it will be either sin or cosine

since we can see the max point is at (0,3) the easiest one to use here is cosine because the cosine graph starts at max ..... or a*cos(0) = a

the general cosine equation is:
\[y = Acos(B(x-h)) + k\]
A - amplitude
B - refers to period -> B = 2pi/period
h - horizontal shift
k - vertical shift

max = 3 , min = -1
A = (max-min)/2 = 2
the midline between max/min is 1 , thus there is vertical shift of 1
k=1

the high points occur at x=0 and 2pi
so 1 cycle takes 2pi --> period = 2pi
B = 2pi/2pi = 1

since cycle starts at x=0, there is no horizontal shift
h=0

\[y = 2\cos(x) +1\]