You're not returning anything even though you said you would. In other words, you're not assigning "root" even though you are trying to return it. Try
% Function to perform Regula-Falsi method
% f is a vector and a and b are indexes to that vector.
% tol is passed in but not used for some reason.
function [fa, fb] = regula_falsi(f, a, b, tol)
fa = f(a);
fb = f(b);
