Use the following function to answer parts a through $c$.
\[
f(x)=7 x^{3}+52 x^{2}+22 x+7
\]
a. List all possible rational zeros.
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Ty

Step 1 ：The Rational Root Theorem states that any rational root, p/q, of a polynomial equation, where p and q are integers, p is a factor of the constant term, and q is a factor of the leading coefficient. In this case, the constant term is 7 and the leading coefficient is 7. So, we need to find all the factors of 7 and 7, and then form all possible combinations of these factors, considering both positive and negative values.

Step 2 ：The factors of 7 are 1 and 7. Therefore, the possible rational zeros of the function are \(\pm \frac{1}{7}\), \(\pm 1\), and \(\pm 7\).

Step 3 ：Final Answer: The possible rational zeros of the function are \(\boxed{\pm \frac{1}{7}, \pm 1, \pm 7}\).