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)

Question

Responses

[−100,100]
left bracket negative 100 comma 100 right bracket

[−100,∞]
left bracket negative 100 comma infinity right bracket

[0,100]
left bracket 0 comma 100 right bracket

[100,∞]

Answer 1

In this scenario, the domain of the function refers to the possible values of the customer’s account balance \( x \) that can lead to the account being locked. The condition states that an account will lock if the balance is less than or equal to \(-100\). Therefore, the values of \( x \) must be less than \(-100\) to trigger the locking condition.

Given the function's criteria, the balance \( x \) can technically take on any values less than \(-100\), as well as more than \(-100\) and up to maximum positive values, but the locking condition only applies when the balance is below \(-100\). Thus, the domain can also be expressed as all values including and greater than \(-100\).

However, the choices provided don't explicitly allow for these values explicitly regarding the locking condition, which nuances the concept of domain in this case.

Among the options provided, none perfectly describes the domain capturing all reasonable values of \( x \). However, the most sensible conclusion from the choices would follow:

• The possible values for \( x \) where the account is affected by this locking condition predominantly suggests that [−100,∞] captures the condition that the function is relevant to all balances above and including -100.

Thus, the correct answer is:

[−100,∞] (left bracket negative 100, infinity right bracket).