### Home > APCALC > Chapter 5 > Lesson 5.3.1 > Problem5-113

5-113.

FUNCTIONS FROM TABLES, Part Two

A function contains the points shown in the table at right. Homework Help ✎

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

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

2. How does the function change? Calculate the finite differences. What kind of function is represented by these differences?

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

$Δy$

$2 − 1 = 1$
$4 − 2 = 2$
$8 − 4 = 4$
$16 − 8 = 8$

3. What is $f \left(5\right)$? Are you sure you are correct?

Also determine the next finite difference term.

 $x$ $f(x)$ $0$ $1$ $1$ $2$ $2$ $4$ $3$ $8$ $4$ $16$ . . . . . .