Tail Recursion: Conceptual

IDentifying tail recursion

For each function identify if it is tail recursive or not and explain why.

(define (f1 x)
    (if (= x 0)
        1
        (if (= (remainder x 2) 0)
            (+ 1 (f1 (- x 1)))
            (+ x (f1 (- x 1))))))

(define (f2 x)
    (define (helper y z)
        (if (= y 0)
            z
            (helper (- y 1) (+ z y))))
    (helper x 0))

(define (f3 x):
    (if (= x 0)
        0
        (f1 x)))

Creating a tail recursive function

Turn the summer function into a tail recursive function. Hint: use a helper function.

(define (summer num)
    (if (= x 0)
        0
        (+ num (summer (- num 1)))))

code Writing

Write a tail recursive function that takes in a list and reverses it.