Final answer:
The rule for the function with the given points is f(x) = x^2 + 2/19, as derived from observing the relationship between x-values and their corresponding y-values where the y-values increase by the square of the x-value with a constant fractional part of 2/19.
Step-by-step explanation:
To find the rule for the function represented by the set of points given, we need to look for a pattern in the y-values relating to the x-values. The provided points are (0,2/19), (1,1 2/19), (2,4 2/19), (3, 9 2/19), (4, 16 2/19), and (5, 25 2/19). Observing the differences between the y-values, it appears that the fractional part remains constant at 2/19, whereas the whole number part increases by the square of the x-value. Therefore, we can express the function rule as f(x) = x2 + 2/19.
Let's verify this by substituting the x-values from the points into our proposed rule:
- f(0) = 02 + 2/19 = 2/19
- f(1) = 12 + 2/19 = 1 2/19
- f(2) = 22 + 2/19 = 4 2/19
- f(3) = 32 + 2/19 = 9 2/19
- f(4) = 42 + 2/19 = 16 2/19
- f(5) = 52 + 2/19 = 25 2/19
As we can see, the values match perfectly, confirming that the rule of the function is indeed f(x) = x2 + 2/19.