Final answer:
Only statement a) g(0) = 1 is universally true for an untransformed parent exponential function with a positive base other than 1. The truthfulness of statements b), c), and d) depends on the specific base of function g, which is not given.
Step-by-step explanation:
We can determine which statements about function g, a transformation of the parent exponential function, are true by comparing to the basic form of an exponential function f(x) = a·bx, where a is the initial value (f(0)) and b is the base of the exponential. First, in an untransformed exponential function where b > 1, g(0) will indeed be 1 since any non-zero number raised to the zeroth power is 1. This makes statement a) g(0) = 1 true if function g has not been shifted vertically. Next, unless g has a base of 1, statement b) g(1) = 1 is not necessarily true as b1 could be any positive number depending on the base b. For the same reason, statements c) g(2) = 8 and d) g(3) = 16 can be true only if the base of g is 2, since 22 = 4 and 23 = 8, the given values do not match the output for a base of 2 exponential function; thus, these statements are false for a parent function without transformations affecting the growth rate. In conclusion, without any additional transformations applied to the parent function, only statement a) g(0) = 1 is universally true for an exponential function with a positive base other than 1.