Find the formula for the graph of the function fxgiven in th

Find the formula for the graph of the function f(x)given in the graph above. f(x) =

mid line : x+a = 4 ; x- a = -2

x = 1; a =3

amlpitude = 3 ; mid line = 1

Let fiunction be : y = acos(bx -c) + k

= 3cos(bx-c) + 1

period = 1/2 ; b = 2pi/(1/2) = 4pi

So, y = 3cos(4pi*x - c) + 1

at x =0 y = 1 ; 1 = 3cos(4pi*0 -c) +1

cos(-c) = 0 ; c = pi/2

So, y = 3cos(4x - pi/2) +1