Worked example: determining domain word problem (positive integers)

Thomas has 400 candy bars in his shop and each costs 50 cents let P of B denote the price P measured in dollars of a purchase of B candy bars alright I input B the number of candy bars I want to buy and P of B will tell me well what's the purchase price it's really she's going to take the number of candy bars and multiply by 50 cents but we don't have to worry about that just yet which number type is more appropriate for the domain of the function so let's just remind ourselves what is a domain of a function a domain is a set of all inputs over which the function is defined so it's the set of all B's it's the set of all inputs over which P of B will produce a defined response so let's think about it is it integers or real numbers so I could buy B could be zero candy bars one candy bars two candy bars all the way up to 400 candy bars could I could I have a fractional K could I could be B 0.37 to of a candy bar well if this is a a normal candy shop it's in each candy bar is going to be in its own packet it's going to be in a discrete chunk you're not going to be able to buy 0.37 to of a candy bar you're either going to buy a one more or not more so you buy 0 1 2 3 all the way up to 400 so I would say integers that the domain of this function is going to be is going to be a subset of integers it's not you're not you can't have a real all real number inputs integers are obviously a subset of real numbers but you can't say hey I'm going to buy PI candy bars I or I'm going to buy the square root of 2 candy bars you're going to buy integer number of candy bars now they say define the interval of the domain so the fewest candy bars I could buy are zero candy bars and I have to decide what do I put a bracket I put a parenthesis so I can actually buy zero candy bar so I'm going to put a bracket if I put a parenthesis that means I could have values above zero but not including zero but I want to include zero so I'm going to put the bracket there so the least I could buy is zero and then the most I could buy the store has 400 candy bars so that's the most I can buy the most I could buy of 400 candy bars and I can buy 400 so I would put brackets there as well so the interval of the domain I would want to select integers so B is a member of integers such that B is also a member of this interval it can be as low as zero including zero and as high as four hundred including four hundred got it right