A "Calvin and Hobbes" Conversation about Algebra

David hasn't looked at math in a year and is brushing up on algebra for a class this fall. He read my favorite book Jacob's Algebra from cover to cover and worked on problems. After finishing the book, he told me how easy it was. He said, "I never realized how much common sense there is in math."

Lately, he has been drilling himself to improve accuracy with a little help from Khan Academy. He got stuck on the concept of the domain of the function  and Sal's video left him even more confused. He came to me for help (I tutor several students during the years so keeping algebra fresh in my head isn't an issue).

Our "Calvin and Hobbes-like discussion cracked me up, so I have to share.

Me: So what are the restrictions on x?

David: x can't equal -2.

Me: Why?

David: Because you would have 0 in the denominator and that is undefined.

Me: Are there any other restrictions?

David: 9.

Me: What does the function equal when x is 9?

David: Undefined.

Me: No, it's 8.

David: 8????? But that makes no sense!

Me: The function is set up so that it equals 8 when x is 9.

David: It's not logical. Why does it do that?

Me: Just pretend it is your mother. "It's 8 because it says so."

David: But, all these years you've been telling me to use logic. This isn't logical. AHHHHH!!!!