![]() When we were saying we were scaling it, we're G of X is equal to negativeġ/4 times X squared. So I'm feeling really good that this is the equation of G of X. When X is equal to four,įour squared is 16. Here 'cause it looks like this is sitting on our graph as well. Two squared is four, times negative 1/4 is indeedĮqual to negative one. When X is equal to one, let me do this in another color, when X is equal to one, then one squared times negative 1/4, well that does indeed look Zero, well this is still all gonna be equal to Our green function, and if I multiply it by 1/4, that seems like it will Okay, well let's up take to see if we could take Well negative one is 1/4 of negative four, so that's why I said Well we want that when X is equal to two to be equal to negative one. When X is equal to two I get to negative four. So how did you get 1/4? Well I looked at when X is equal to two. ![]() So in that case, we're gonna have Y is equal to not just negative X squared, but negative 1/4 X squared. See if we scale by 1/4, does that do the trick? Scale by 1/4. When X is equal to two Y is equal to negative four. So you could say G of two is negative one. When X is equal to two, Y is equal to negative one on G of X. ![]() Here that at the point two comma negative one, sits on G of X. ![]() This is to pick a point that we know sits on G of X,Īnd they in fact give us one. That it does that stretching so that we can match up to G of X? And the best way to do And so let's think about,Ĭan we multiply this times some scaling factor so G of X also seems to be stretched in the horizontal direction. Whatever X is, you square it, and then you take the negative of it, and you see that that willįlip it over the x-axis. Whatever the X is, you square it, and then you take the negative of it. To the negative of F of X, or we could say Y is equal ![]() So this green function right over here is going to be Y is equal Getting before for a given X, we would now get the opposite So as we just talk throughĪs we're trying to draw this flipped over version, whatever Y value we were Y when is X is equal to negative two instead of Y being equal to four, it would now be equal to negative four. Take the negative of that to get to negative one. Instead of squaring one and getting one, you then But when X is equal to negative one, instead of Y being equal to one, it'd now be equal to negative one. Instead when X is equal to zero, Y is still gonna be equal to zero. So first let's flip over, flip over the x-axis. We might appreciate is that G seems not only toīe flipped over the x-axis, but then flipped overĪnd then stretched wider. So like always, pause this video and see if you can do it on your own. G can be thought of as a scaled version of F ![]()
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