FUNCTIONS FROM TABLES, Part Two

Find a function, $f(x)$, that fits the table shown below.

1. What kind of function does this appear to be? Find a possible equation.

   Hint (a):

   Is it linear? Quadratic? Cubic? Exponential? Something else?

2. How does the function change? Find the difference between the terms in $f(x)$, what kind of function is represented by these terms?

   Hint (b):

   What pattern do you see among the finite differences ($Δy$) pattern?

3. Find $f(5)$. Are you sure you are correct?

   Hint (c):

   Also determine the next finite difference term.