A bank uses an automated function in which a customer’s accounts will lock if they owe more than $100. Consider an equation where x is the balance of a customer’s account. What is the domain of this function?(1 point) Responses [100,∞] left bracket 100 comma infinity right bracket [−100,100] left bracket negative 100 comma 100 right bracket [−100,∞] left bracket negative 100 comma infinity right bracket [0,100]

Question

GPT-4o mini · Answer

In this scenario, the equation refers to the balance $ x $ of a customer's account, where the bank locks the account if the balance $ x $ is less than $-100$ (i.e., if the account is overdrawn by more than $100). Therefore, we need to consider the possible values of the account balance.

The domain of the function, in this case, is the set of possible values for the account balance $ x $. Since balances can theoretically go as low as negative infinity (for accounts that are heavily overdrawn) and can also be any non-negative value (indicating a positive balance), the domain of this function is:

\[ (-\infty, 100] \]

However, it looks like the given options do not include this. Among the available choices, the only reasonable option is:

[-100, ∞)

This means that the balance could range from -100 and can include values above, where the total balance could be positive. Note that we interpret -100 as being on the edge of locking and hence permissible right at this boundary.

Thus, if we look at the nature of the balance locked here, the correct response would lean toward:

\[-100, ∞\]