Linear Equation

T can't be less than zero, because in this situation, negative years would be meaningless.

This is simply just defining a function along with the domain of the function.

There is no reason T can't be greater than 6 or less than 0. This function simply doesn't apply for values outside of this domain.

It is by definition.

I disagree with Brandon. There is no problem in thinking of negative years. I have no problem telling you the value of my car two years ago.

What about two years before it was manufactured.

There’s nothing in the question to say it’s new or second hand. If it’s brand new it won’t have existed two years ago.

That's why I said "in this situation." No one calculates depreciation on property backwards to before they obtained it. I never claimed there was generally no use for negative time.

There are a couple of interesting topics here. I am specifically responding as a teacher in the subject of mathematics. I am not that interested in price of a car.

1) In the OP NYCDad defines a function. He uses the term "equation", but the term equation is misleading. This is one of my pet peeves in math education... teachers use the term "equation" because students studied "equations" in middle school. It is a shortcut that hurts the students level of understanding.

2) The depreciation function is abitrary. Someone makes them up. It is a rule invented for legal and accounting purposes. It doesn't say anything measurable. That is the logical reason it ends after 6 years.

3) When you write down a function, you are defining that function. Whether the function you defined correctly models something in real life is another issue. The function exists in itself as a mathematical entity, The domain is part of the function definition.

If I say f(x) = 2x + 3 for -2 < x < 10. This is a perfectly valid, and well defined function. I just made it up, I don't really have any real life propblem in mind. And yet I can use this function the same way I use any other function.