Determining the domain of a function
Thomas has 400 candy bars in his shop and each cost 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 candy bars I wanna buy, and p(b) will tell me what's the purchase price is really just taking the number of candy bars multiplied by 50 cents, but we won't have to worry about that just yet. Which number type is more appropriate for the domain of the function? So just to remind ourselves, what is the domain of a function? A domain is a set of all inputs over which the function is defined. So it is the set of all b's. It is 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 0 candy bars, 1 candy bars, 2 candy bars, all up to 400 candy bars. Could I -- Could I have a fractional can-- Could be b 0.372 of a candy bar? Well, this is a normal candy shop. It's -- each candy bar is gonna be in its own packet. It's going to be in a discrete chunk. You're not going to be able to buy 0.372 of a candy bar. You can either buy a one more or none more, so you buy your 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 not, you can't have a real, all real number, but integers are obviously a subset real numbers. But you can't say, hey, I'm gonna buy pi candy bars, or I'm gonna buy the square root of two candy bars. You're gonna buy integer number candy bars. Now they say, define the interval of the domain. So the fewest candy bars I could buy are 0 candy bars, and I have to decide whether I put a bracket or I put a parenthesis. I can actually buy 0 candy bars so I'm gonna put a bracket. If I put a parentheses, that means I could have values above zero but not including 0, but I want to include 0 so I'm gonna put the bracket there. So the least I could buy is 0, and in the most I could buy, the store has 400 candy bars so that's the most I can buy. The most I could buy are 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 could be as low as 0 including 0, and as high as 400 including 400. Got it right.