The following is a recursive Python function:

Question

def mystery(n):
if n == 1:
return 3
else:
return mystery(n - 1) + 3

Which mathematical function is defined recursively by this Python function?

(1 point)
Responses

3+n
3 plus n

3
3

3⋅n
3 times n

3+(n−1)

Answer 1

The provided recursive function can be analyzed as follows:

• When n is 1, the function returns 3.
• For any other value of n, the function calls itself with n - 1 and adds 3 to the result.

This means that the function calculates:

• For n = 1: mystery(1) = 3
• For n = 2: mystery(2) = mystery(1) + 3 = 3 + 3 = 6
• For n = 3: mystery(3) = mystery(2) + 3 = 6 + 3 = 9
• For n = 4: mystery(4) = mystery(3) + 3 = 9 + 3 = 12
• And so on...

We can see that for n, the function returns \(3 + 3(n - 1)\). This is because each reduction in n adds 3, effectively making it \(3 \times n\).

Thus, the mathematical function defined by this recursive function is:

3 times n (or mathematically represented as \(3n\)).