What Is the Domain of a Function?

$$\text{Tell a Story Day}$$

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Today (April 27) is national tell a story day!

There once was a prince who lived in a castle with his mother and father. He lived a happy life, but it was a lonely one. The king was so paranoid about losing his son that he forbade him from ever leaving the castle. For years, the prince grew up watching the other kids play outside from his window.

On his 17th birthday he finally had enough, and that night he sneaked out of the castle. Immediately, a giant and terrible dragon swooped down and picked him up. The prince yelled for help, but it was no use, the dragon flew him back to its lair.

See, dragons are wise creatures. It knew that it could use the prince in order ransom what it wanted most from the king: gold. The dragon sent a message to the king (yes dragons can send messages) telling him he wanted all his gold and in return he would see his son again. The king, with no other option, gave all his gold to the dragon. But dragons are also tricky creatures. It held its end of the bargain by flying the prince by the king's window so the king could see the prince again. After that, the dragon took him back to its lair. The king was devastated.

In the passing months the king tried to hire brave knights to slay the dragon and save the prince, but he had no gold to offer so they all turned him away. But one day a young woman approached the king. She said she would return the prince under one condition: she could take the prince's hand in marriage. The king, doubtful, still agreed and that night the woman set out to the dragon's lair.

The woman arrived at the mouth of the dragon's lair. The air was hotter and smelled of death and lavender. Dragons actually try very hard to smell nice but sadly it rarely helps. The woman took a deep breath (through her mouth, not her nose) and entered the lair empty handed.

The dragon was red and scaly and smelled overly strong of lavender. Seeing the woman approach without any weapons, it regarded her with curiosity.

"Are you lost little girl?" it asked.

"I've come for the prince," the young woman demanded.

"And you expect me to just hand him over? I could just kill you here and now."

"I've read that dragons are wise creatures."

"This is true," the dragon smiled, or the closest thing to a smile that a dragon can give.

"Then I propose a challenge."

"What kind of challenge?" The dragon was intrigued and lowered its head until it was face to face with the woman.

"You ask me three questions. If I miss any of them, you get to eat me right here, right now. But, if I can answer all three correctly, you have to let me and the prince go."

The dragon took a second to think about her proposal. Finding it more than fair, it agreed. They didn't shake hands or anything because dragons don't have hands.

"First question. What is my name?"

The woman was prepared for this question because she too was very wise. She had read up on the history of the kingdom and found the dragon's name a long time ago. "Reginald."

The dragon narrowed its eyes. "Correct. Question two. How long do you need to travel east to reach the edge of the world."

The woman had been reading up on scientific theories since she was 12 and wasn't faltered. "This is a trick question. The world isn't flat. It is round."

The dragon gave a low growl, all the while never removing his eyes from hers. It was clearly growing more annoyed. It pondered the final question for a long while. Finally, it spoke.