Question

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

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

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

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

[100,∞]

Answer 1

The domain of the function in this scenario is determined by the possible values of the account balance \( x \) that could affect whether the account is locked or not.

Since the account locks if the balance is less than or equal to -100 (indicating that the customer owes more than $100), we are interested in values of \( x \) that can be less than or equal to -100 or greater than -100 (which would mean they owe less than $100).

Therefore, the domain of this function should include all balances that are less than or equal to -100 and anything above that.

The correct response is:

**[−100, ∞]**

So, the account could be locked if \( x \leq -100 \) or unlocked if \( x > -100 \). The necessary values to account for this are from -100 to +∞, including -100 itself.