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Current time:0:00Total duration:3:16

CCSS.Math:

G of X is a transformation of f of X the graph here shows this is y is equal to f of X two solid blue line this is y is equal to G of X as a dashed red line and they ask us what is G of X in terms of f of X and like always pause the video and see if you can give a go at it and then we're going to do it together alright so when you immediately look like it looks like G of X is kind of a thinned up version of f of X it seems like if you were to compress it to towards the center that's what G of X looks like but let's put a little bit more meat on that bone and see if we can identify corresponding points so for example if we were to look at f of negative 6 that's so f of negative 6 that seems like it corresponds or gives us the same value as f of negative 6 and we want to find the corresponding point so we've hit this minimum point we're coming back up hit the minimum point we're coming back up it seems like the corresponding point right over there is G of negative 3 so let's write that down let's see it looks like F of negative 6 and it is equal to G of negative 3 these are corresponding points if you apply the transportation at the point f equals at the point negative 6 comma F of negative 6 you get to the point negative 3 G of negative 3 right over there let's do a couple of more if you look at F is so f of 2 looks like it corresponds to G of 1 F of 2 corresponds to G of 1 so let's write that down f of 2 looks like it corresponds to G of 1 and once again I'm looking at the where the functions hit the same value and also optically I'm just looking at what it looks like it's the same part of the function if we assume G of X is a squeezed version of f of X and so in general it looks like it looks like for given X so we could say f of X is going to be equal to G of well whatever you have in here it seems like we have half the value over here so G of x over 2 or if you wanted to think of it the other way if you wanted to think of the other way if you want to say G of X is going to be f of well whatever we have here it's f twice that so F of 2x and we see that that is one of the choices that G of X is equal to F of 2x whatever the X that you input into G of X you get that same value out of the function when you input two times that into f of X and these these seem to validate that it looks optically like that that we shrunk it down one way to think about it when you take when you multiply the the input into a function by a number larger than then one it's going to compress it's going to make things happen faster the input to the function is going to increase or become negative faster so it's true it thins it up and if that doesn't make intuitive sense you can also just try to try some of these values and I encourage you to try more find the corresponding points where the F's and the G's seem to match up and you'll see you over and over again that to get the same value you have to put two times as much into F as you have to put into G hopefully that helps