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CCSS.Math: , ,

match each function with its graph and we have graph D a B and C and let's just start with the graph of B because actually this little looks the closest to the square root of x which would look something like that but it's clearly shifted and it's flipped over the horizontal axis the fact that it's flipped over the square horizontal axis that means that we're taking the negative square root we're taking the negative square root so it's going to be one of these two cases right over here we're shifting it down by two so we should have a negative two and both of these cases have a negative two here and we're shifting it relative to the square root of x we're shifting it to the right by one so if we're shifting to the right by one what we see under the radical should be X minus one and both of these have an X minus one on it so which of these is B and which of these is C and I encourage you to think about that pause the video if you if you like well the difference between these two is this one has a scaling factor of 2 here while this one doesn't so this one and it's and of course this is going to turn into more and more negative values this is going to be getting negative faster and you see that graph C here gets negative faster and you can even try some points in either case when X is equal to an x is equal to 1 in either case what we have under the radical becomes 0 X minus 1 is 0 X minus 1 is 0 when X is equal to 1 and in either case our Y value is negative 2 but then you see as x increases as x increases this one right over here gets negative twice as fast and you see that right over here this one this one right over here relative to our starting this this has gone down relative Y has gone from negative 2 to negative 4 here while for the for graph see Y has gone from negative 2 to negative 6 so it's gone down by 4 this has only gone down by 2 so it's pretty clear that graph B corresponds to the one that doesn't have the 2 out front so this is graph B right over here and graph C corresponds to the one that has the negative 2 out front so let me throw that the negative 2 out front so now we just have to think about these two graphs or these two equations and match them to these two graphs and so both of these they they haven't been flipped around the horizontal axis they've been flipped around the vertical axis and that's why whatever we have under the radical we've essentially taken the negative of it and actually we could figure out which which ones these are just by looking at how much they've been shifted in the y-direction relative to the square root of x which would be which would look something which would look something like something like that I know you can't draw I can't drawn this one right over here well this one has been shifted up by two D has been shifted up by two this one over here G of X has been shifted up by two and you could also see that it's been shifted to the left by one if you're shifting to the left by one normally under the radical you would have X plus one but then we flipped it over on to on around the vertical axis and so that takes the negative of that so that's why it's negative X minus one you could view this as the negative of X plus one so either way that is d that is d throw that under two D and this deductive reasoning this tells us say that this is a and it makes sense we see it is shifted up by one so it's plus one and we could view this as as the negative as the negative of X minus four as the negative let me as the negative of X maybe the negative of X plus four so it's been shifted four to the left and we see that is definitely the case relative to the square root of x we got it right