We can try to find the funtion by the given data or replace in the answers and see what is the answer, we are going to do both.
Usually when we try to find a function we try to find patterns in the data, in this case in the energy
We have that 4 is send to 66, now we can try to find a relation between 4 and 66 but first we see all the data 5 is send to 77 and 6 to 88. With this we can see that the difference between the energy in 4 and 5 is 11 that is the same difference betwen the energy in 5 and 6, so if pass one more minute the energy increase 11. So we have that f(6) = f(4) + 22 and f(5) = f(4) +11.
With this we can find the initial charge. we now that if pass 4 minutes the energy is going to increase 11 * 4 = 44 if we take the initial point at the minute 4 the funtion is going to be f(0) + 44, this is f(4) = f(0) + 44 and we know the value of f(4) that is 66, now f(0) = 66 - 44 = 22 with this we have that the function is f(x) = 11*x + 22 .
We are going to replace x by 4 in every fuction to verify the answer
a) f(4) = -11/10 * 4 + 22 = -4.4 + 22 = 17.6 so is not 66, this is not the function
b) f(4) = 11/10 * 4 + 22 = 4.4 + 22 = 26.4 so is not 66, this is not the function
c) f(4) = 11*4 + 22 = 44 +22 = 66 this could be the function
d) f(4) = 11*4 + 66 = 44 + 66 = 110 so is not 66, this is not the function
Then the answer is c) f(x) = 11*x + 22