Answer:
f(x) = 9x + 4
Step-by-step explanation:
Consider the output values
13, 22, 31, 40, 49
The difference between consecutive terms is constant, that is
22 - 13 = 31 - 22 = 40 - 31 = 49 - 40 = 9
This indicates the function is of the form
y = 9x + c ( where c is a constant )
To find c substitute the values of the input
x = 1 : y = 9(1) + c = 13 → 9 + c = 13 ⇒ c = 4
x = 2 : y = 9(2) + c → 18 + c = 22 ⇒ c = 4
x = 3 : 9(3) + c = 31 → 27 + c = 31 ⇒ c = 4
x = 4 : 9(4) + c = 40 → 36+ c = 40⇒ c = 4
x = 5 : 9(5) + c = 49 → 45 + c = 49 ⇒ c = 4
The value of the constant is 4
Thus the function representing the data is f(x) = 9x + 4
