Given the function \( f(n) \) defined recursively as:

\[
f(0) = -23
\]
\[
f(n) = f(n-1) + 4 \quad \text{for } n > 0
\]

This means that each subsequent value of \( f(n) \) is obtained by adding 4 to the previous value of the function. 

### Let's calculate the first few values of \( f(n) \):

- \( f(0) = -23 \)
- \( f(1) = f(0) + 4 = -23 + 4 = -19 \)
- \( f(2) = f(1) + 4 = -19 + 4 = -15 \)
- \( f(3) = f(2) + 4 = -15 + 4 = -11 \)
- \( f(4) = f(3) + 4 = -11 + 4 = -7 \)

### General formula:
We can also express \( f(n) \) using a formula:
\[
f(n) = f(0) + 4n
\]

Substituting \( f(0) = -23 \):
\[
f(n) = -23 + 4n
\]

This is the explicit formula for \( f(n) \).

Would you like more details on this or have any questions?

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Here are some related questions:
1. What would \( f(10) \) be using the general formula?
2. How would the function change if the initial value was different?
3. How can you determine the value of \( n \) when \( f(n) = 0 \)?
4. How would the recursion change if the increment was a different value, say 5?
5. What is the significance of the recursive definition in general problem solving?

**Tip:** Understanding recursive functions helps in tackling complex problems by breaking them into simpler, repetitive steps.

Explore the recursive function f(n) = f(n-1) + 4, starting with f(0) = -23. Learn how to calculate specific values and derive the general formula for f(n). Suitable for students in Grades 9-10, covering recursive definitions and arithmetic sequences.

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