Answer:
y = 3 -5sin((π/2)x)
Step-by-step explanation:
We notice the function is periodic with a period between minima of (5-1)=4. It has a maximum of 8 and a minimum of -2, so for the form ...
y = Asin(kx) +C
the value of A is ...
A = (1/2)(8 -(-2)) = 5
and the value of C is ...
C = (1/2)(8 +(-2)) = 3
The function is at its middle position (3) at x=0, and is headed downward toward -2 at x=1, so can be modeled by the opposite of the sine function. That is, an appropriate value for A is -5.
The value of k is ...
k = 2π/period = 2π/4 = π/2
Then the possible formula for the function is ...
y = -5sin((π/2)x) +3
