Final answer:
The range of the function g(x) = 500(1.06)^x representing the balance of a savings account earning annual interest is [500, ∞), indicating the balance will start at $500 and can grow indefinitely.
Step-by-step explanation:
The range of a function represents the possible output values of the function. In the context of the problem, where you deposit $500 into a savings account that earns interest annually, the function g(x) = 500(1.06)^x is used to calculate the balance in the account after x years. Since the account earns interest, the balance will never decrease; it will either stay at $500 if x is 0, or increase as x grows. Therefore, the range of the function in this context begins at the initial deposit amount of $500 and extends indefinitely as more interest is earned over the years.
Thus, the range of this function is [500, ∞), which means the balance will be at least $500 and can grow without bound as time passes and more interest accrues.