Question

what is a rule for the function represented by (0, 2/19), (1, 1 2/19), (2, 4 2/19), (3, 9 2/19), (4, 16 2/19), and (5, 25 2/19)? Explain your reasoning

Answer 1

Notice
\[
f(0)=\frac 2 {19} = 0^2 +\frac 2 {19}\\
f(1)=1+ \frac 2 {19} = 1^1 + \frac 2 {19}\\
f(2)=4+ \frac 2 {19} = 2^2 + \frac 2 {19}\\
f(3)=9+ \frac 2 {19} = 3^2 + \frac 2 {19}
\]
What can you conclude?

Answer 2

\[
f(4) = 16 + \frac 2 {19} = 4^2 + \frac 2 {19}\\
f(5) = 25 + \frac 2 {19} = 5^2+\frac 2 {19}
\]

Answer 3

So
\[
f(x)= x^{?} + ?
\]