The correct answer is B. has to.
The verb “have to” is used to express obligation or necessity. In this case, the speaker is asking whether the woman has an obligation to get up early and cook for her family. The answer is yes, she does have to do this, because she is old and her family depends on her.
The other options are not correct because they do not express obligation or necessity. The verb “is” is used to describe a state of being, and the verb “had” is used to describe a past action. The verb “to” is a preposition, and it is not used in this context.
Here are some examples of how the verb “have to” can be used:
- I have to go to the store.
- You have to do your homework.
- We have to be at the airport by 8:00 AM.
- They have to finish their project by the end of the week.