# Functions from tables (using finite differences)

## Function f

Give a quadratic function that would result in the values given below. Compute the missing value.

$$x$$ $$f(x)$$
1 2
2 6
3 12
4 20
5
100

## Function g

Give a quadratic function that would result in the values given below. Compute the missing value.

$$x$$ $$g(x)$$
0 0
1 5
2 12
3 21
4 32
137

## Function h

Give a quadratic function that would result in the values given below. Compute the missing value.

$$x$$ $$h(x)$$
1 -4
3 1
5 12
7 29
9 52
11 81
141

## Function j

Give a linear function that would result in the values given below.

$$x$$ $$j(x)$$
3 25
4 23
5 21
6 19
7 17
8 15

## Function k

Unfortunately this method will not always work. Why won't it work in the example below?

$$x$$ $$k(x)$$
0 1
1 2
2 4
3 8
4 16
5 32

## Challenge: Function m

Give a polynomial function that would result in the values given below. Compute the missing value.

$$x$$ $$m(x)$$
0 2
1 3
2 6
3 12
4 22
100