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Current time:0:00Total duration:5:34

Worked example: determining domain word problem (all integers)

CCSS.Math:

Video transcript

this right over here is a screenshot from a Khan Academy exercise and it says Mason stands on the fifth step of a vertical ladder the ladder has 15 steps and the height difference between consecutive steps is 0.5 meters he is thinking about moving up down or staying put so let me draw this this this ladder that Mase isn't that Mason is on so it's a vertical ladder so that's one side of the ladder this is the other side of the ladder and it has 15 steps let me see if I can draw that so this is the first 1 2 3 4 which I'm going to run out of space I need to make them closer together so it's going to be 1 2 3 4 5 6 7 8 9 10 11 12 13 14 and 15 15 15 steps let me make sure it's even so the top of the bottom and the difference the the distance between each of these I guess you could say steps or the rungs of the ladder are half a meter so this distance right over here is 0.5 meters and it says that he's on the fifth step of this vertical ladder so he's on the fifth step so 1 2 3 4 5 so this is where he is right now he's on this fifth step and he's thinking about moving up or down or staying put let H of n denote the height above the ground H of Mason's feet F measured in meters after moving n steps if Mason went down the ladder and is negative all right H of n so when so when he is the height above the ground after moving n steps so let's just as a make sure we understand this if I were to say H of 0 what is that going to be well H of 0 means that he's moved 0 steps he's moved 0 steps he's still going to be on this fifth step of the ladder and so how high is he going to be so if he's on the 5th step of a vertical ladder so he is going to be so I'm assuming that there's 0.5 from the ground so this is the ground right over here so he is 1 2 3 4 5 steps each of them is half a meter so 5 times 0.5 is going to give us 2.5 meters so H of 0 is 2 point 5 meters if I said H of 1 that means he goes up H of 1 means he goes up one step so here n would be equal to 1 so if it goes up 1 step H of 1 he's going to be 1/2 a meter higher so is going to be equal to 3 meters so we could keep doing that for a bunch of different inputs so let me write that that's going to be equal to 3 meters but anyway that's not what they're asking us about they're saying which type which number type is more appropriate for the domain of the function so the domain that just as reviewed that's that's the set of numbers that we can input into the function and get a valid output and it's clear here so we have to pick between integers or real numbers well n which is our input that's the number of steps you goes up or down so it could be positive or negative but we're not we're not going to talk about half step C then he'll put his foot in the air right over here he has to take integer valued steps up or down or I guess he's taking integer value steps if it's positive it's up if it's negative it's down if it's zero that means he's staying put if n is zero that means he's staying put it's not real numbers he can't take he can't take he can't move pi steps from where he is he can't move square root of 2 steps from his he can even move point 0.25 steps then hit put his foot in the air so this is definitely going to be about the integers not the real numbers this function right over here the valid inputs if I want to be able to input an integer in fact it's not even all integers because he can't go down an arbitrary amount in fact Li he can't go up an arbitrary amount either but it's going to be the domain is going to be a sub set of integers and then they say define the interval of the domain and we have these little toggles here to to to think about to define the interval of the domain and let's see the lowest value for n he can go as far as 1 2 3 4 5 steps down and in that case n would be equal to negative 5 and then the highest value for n is if he takes 1 2 3 4 5 6 7 8 9 10 steps up and so that would be n is equal to 10 so the interval of the domain and actually I'm just using I just copy and pasted this onto my scratch pad he can n can be as low as negative 5 and as high as 10 and it can include them as well so I'm going to use brackets so my domain would include negative 5 if it didn't include negative 5 output of parentheses but I could put brackets here and I could put brackets there as well and I can actually let me just for fun let me actually input it into the actual exercise so I'm saying integers and I'm as low and can I can go down 5 steps and I can go up 10 steps and 10 is also included in my interval then I could check my answer and I got it right