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Current time:0:00Total duration:5:15

Video transcript

what I want to do in this video is think about how does the value of an expression change as a variable that makes up that expression changes so let's start with a pretty simple expression let's say we have the expression 100 minus X we want to know how does this expression change as x increases as x increases and like always try to work it out for yourself pause the video before I try to have a go at it well there's a couple of ways you could think about it you say okay I have a hundred and I'm subtracting X so as x increases as x increases over here I'm going to be subtracting larger and larger values so if I'm subtracting larger and larger values I'm going to get smaller and smaller values so this whole thing this whole thing is going to decrease this whole thing is going to decrease and if you want to make it a little bit more concrete you can actually try out some values there so you can make a little table here X and then what is 100 minus X going to be and I'm just going to pick some values of X I'm going to make them increase say X is 0 X is 50 X is 100 well when x is 0 100 minus X is 100 minus 0 so it's 100 when X is 50 it's going to be 100 minus 50 so it's going to be 50 when X is 100 it's 100 minus 100 so it's 0 so it's pretty clear here that as X is increasing as X is increasing I'll just write inker for short for increasing we see we see that 100 minus X is decreasing we see that that is decreasing let's do this with a couple of more expressions that have different forms so let's say that I have the expression let's say that I have the expression 5 over X plus 5 and X is decreasing X is decreasing but we also know that it is positive and it's and even while it's decreasing it's staying above zero so we're saying X is staying greater than zero so in this case so you know this could be a situation where X is decreasing from 10 to 9 or a million a hundred thousand but it's staying positive while it's decreasing well let's think about that we are going to be dividing by smaller and smaller positive values so as you decrease as you as you have smaller and smaller positive values in the denominator you're dividing by smaller and smaller positive values so if you're dividing by smaller positive values you're going to this thing is going to get larger this entire expression is going to get larger as you divide by smaller and smaller positive values so if that expression gets larger then you're just adding five to it the whole thing is going to increase the whole thing is going to increase as the whole thing is going to increase as X decreases while staying positive and once again we could make a little table to take a look at that so if this is X this is five over X plus five and let's see I'll just try out some let's see if X I'll go from X code 100 to X is 2 X is 5 2 X is 1 so this is clearly X is decreasing X is decreasing when X is 100 you're going to have 5 divided by 100 which would be 5 hundredths plus 5 so it'd be five point zero five when X is five you're going to have five divided by five which is 1 plus 5 which is 6 and 1 and what X is 1 you're going to 5 divided by 1 which is 5 plus 5 is 10 so notice when X is staying positive but decreasing the whole expression 5 over X plus 5 this thing right over here is increasing increasing let's do one more of these so let's say that we have the expression and we'll change up the variable here 3y over 2y and I'm curious what happens to this about the value of this expression as Y as Y increases as Y increases well as is as you have larger Y's here on the numerator you're also going to have larger Y's here in the Nam and one way you could think about this this is the same thing as three halves times y over y and no matter what y you have here as long as it's not equal to zero and actually let's just assume that it doesn't cross zero because at that point at that point this thing would become undefined let's just say that Y increases in Y is greater than zero just for simplicity so y is y is a positive value here and actually for any positive for any nonzero value you take Y you divided by Y you're just going to get one so it doesn't matter what Y is y could be a million over a million this thing is just going to be one Y could be five over five is still just going to be one the value of the expression is not going to change it's just going to be three halves so the expression is going to be the same you're going to you're not going to have any change as Y increases as Y is positive and it increases