Question

An observer atop a cliff sees a speedboat approaching a dock located at the base of the cliff directly below the observer. Express the distance, d, from the observer tot he boat as a function of the distance, x, from the boat to the dock, if the cliff is 150 feet high. State the domain.

I have answered the first part of the question:
d=sqrt(150^2 + x^2)

I am confused about the domain part. I thought the domain would be (-infinity, infinity) but the answer key I have says it is x>0.

Can someone explain?

Answer 1

clearly, real-world distances cannot be negative.

You have to use a little common sense along with the math.

Even if you allowed for negative distance, that would mean the boat burrowed into the cliff!