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,∞]
left bracket 100 comma infinity right bracket

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

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

[−100,100]

Answer 1

To determine the domain of the function based on the condition given (a customer's account will lock if they owe more than $100), we need to consider what values of \( x \) (the balance of the customer's account) will cause the function to be defined.

A customer owes more than $100 if their balance is less than -$100. This means that the account will not lock for balances greater than or equal to -$100, including all balances that are $0 or more (positive balances) as well as any negative balance that is less than -$100.

Given this, we can conclude that the balance could range from -$100 to positive infinity. Thus, the domain of this function would be represented as:

\[ [-100, \infty) \]

Therefore, the correct choice is: [−100,∞].