Question

Use the middle column in each of the given tables to write the process or number patterns that

relate the input to the output. Then create both a recursive and explicit function rule.


Recursive:
Explicit:

Answer 1

the recursive function rule for the given number pattern is f(n) = 3 * f(n-1), with an initial value of f(1) = 3. The explicit function rule is f(n) = 3n, with an initial value of f(1) = 3.

Explanation:

To find the process or number patterns that relate the input to the output:

- For each value of n, the output f(n) is obtained by multiplying the input by 3.

- The pattern is that each output f(n) is three times the value of the input n.

Using this information, we can create both a recursive and explicit function rule:

Recursive Function Rule:

To generate the next value in the sequence, multiply the previous value by 3.

f(n) = 3 * f(n-1)

f(1) = 3

Explicit Function Rule:

The explicit function rule represents the relationship between the input and the output directly without relying on previous values.

f(n) = 3n

f(1) = 3