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5-113.

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.

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

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

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

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

Also determine the next finite difference term.

$x$

$f\left(x\right)$

0

1

1

2

2

4

3

9

4

16

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