Domain in Practical Situations

[fleet street]

Hi everyone,

I've got an Applications SAC coming up really soon and I've noticed that I seem to be hopeless at finding domains.

Example: A car is driving along (from left to right) along a highway that is modelled by . A statue is at . It can be shown that the Distance (D) between the statue and a general point (b) on the highway is given by Draw a graph of D versus b over a suitable domain.

I assumed that the domain would be all real numbers, but the solutions say:

An appropriate domain is any subset of, that includes
the turning point (since the tangent to the curve passes through the coordinates of the statue for
and ).

I was wondering whether anyone could make any sense of this, and, furthermore, if there was a general way of going about finding domains.

Thanks!

[BubbleWrapMan]

Yeah, I can't see a reason to restrict it either. I'd wager that it's not so much that you're hopeless, but more that the questions you're doing aren't worded\written well. That last point in the solutions seems to have been plucked from the aether; there's no way you'd be expected to give that sort of an answer without any prompt.

[fleet street]

Thanks! I actually have the calculus part of my SAC tomorrow, so you made me really relieved just in time!