Question

Given f(n) = f(n-1) + 2; f(1) = -7, write an explicit function rule.

Answer 1

To write the explicit function rule for the recursive function f(n) = f(n-1) + 2, with f(1) = -7, we can observe that the output values increase by 2 for every increase in n. This allows us to write the explicit function rule as f(n) = -7 + 2(n-1).

Step-by-step explanation:

The given function is a recursive function defined by the equation f(n) = f(n-1) + 2, with an initial condition f(1) = -7. To write the explicit function rule, we need to find a formula that directly relates the input n to the output f(n).

We can observe that the output values of f(n) are increasing by 2 each time the input n increases by 1. This means that the difference between consecutive output values is always 2.

Using this information, we can write the explicit function rule as f(n) = -7 + 2(n-1).