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The graph ofil) = zk show he nzhz; Detenine tha graph TV-z+1.Chonge thB comect grph belaw:...

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The graph ofil) = zk show he nzhz; Detenine tha graph TV-z+1.Chonge thB comect grph belaw:

The graph ofil) = zk show he nzhz; Detenine tha graph TV-z+1. Chonge thB comect grph belaw:



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Graph $y=\frac{1}{x^{2}}$ on the viewing window $[-0.5,-0.1]$ and $[0.1,0.5] .$ Determine the correspondinge for the viewing window. Show the graphs.

You know this problem we want to use the graph of Y. Is equal to eat the acts to graft to other functions. Now if we're gonna use the graph of Y equals E. To the X. Let's go ahead and graph it. I don't really know what our starting point is. Well actually the X passes through the .01 and then it's an increasing exponential function. And so it looks something like that. Yeah. Now in a we would like to draft F. Of X. Is it really E to the negative to action since we have that and give to in the next one. Now that negative if you remember is ayla reflection across the Y axis. And so you're gonna take that original function reflected across the Y axis. And then the two is what's called a horizontal stretch. And so it's trying to make it go down or quicker and up quicker. And so started here. It's going to go something like this. We reflected it over the Y axis and we made it go down quicker and quicker on B. We have F. Of X. Is equal to negative two E. To the X. Now here that negative is going to flip it across the X. Axis. So it's going to put it down in the third in the fourth quarter. And then that too on the outside is what is called vertical stretch. And so it's still going to make it go up quicker and quicker. So here again we reflected that black curve across the X. Axis and so it's going to look something like that. They're in red.

Yeah. Yeah. So you want to scratch the, you know, uh the inverse function, right. Given the graph uh shown. Right. So what is the inverse function? Well, the sketch of the universe function is just gonna be this whenever you have a graph uh function. Okay. And you have eggs? Why write a graph? Every graph is made of the X coordinate and the Y coordinate. The inverse function of the graph is just gonna be a swap of the coordinates. So it's not it's not gonna be Y. X. So that's why it's going to take the X coordinate. And this is gonna take the white coordinate. That is how you sketched the the inverse graph. Right? So just look at the coordinates of the graph given the question and flip the coordinates right? The X coordinate of the graph itself is going to be the y coordinate of the universe graph. And they y coordinate of the graph itself is going to be the X coordinate of the universe graph. That's it. So if you flip all the coordinates, you can see that this is gonna be your inverse graph. Uh It's going to be going to look something like this. Mhm. Let me see here. It's going to look something like this, right? It's not drawn to scale, but this is what it's gonna look like, right? Yes. And then you want to find uh you know, you want to estimate f inverse prime of three. So there's this relation, you know, F universe prime, oh three is the same as one over F of F in verse three. Okay, this relation is what you're gonna use. So what is F inverse of three? So look at your inverse grab, this is my invoice graph, right? You're gonna have the labels So when you uh do the, You know, FM 1st crime of The f inverse of three. Okay. Uh huh. Uh huh. You can find you you got to find this one after that you find f of the result in thing, And then you divided by one. Right? You divide you make it one all of that thing. You can see that it's going to be one of the three, right? It means that this thing here is going to be three. Do you know why? Because f universe the coordinate is 34. Right? So uh F Inverse of three is four, And every four is 3. So the bottom here is going to be three. So it's 1/3. Right? But the most important thing is this relation. Do not forget that this is important relation. So whenever you use this relation and the combination with the grab, you can see that this is gonna be the f inverse prime of three.

Yeah. So you want to sketch the uh inverse graph, right? Using the graph given, like I said, uh the inverse graph is the swap of the graph itself. So whenever you have a coordinate, whatever coordinate that is used in the in the graph given in the question when you have an X coordinate and Y coordinate, they both combined to give you a point on the graph in the question. So take any point on the uh graph in the question. And you can see that you're gonna have an X coordinate and y coordinate. The inverse one is just gonna be a swap. So the y coordinate is not going to turn into the X coordinate and then the X coordinate is going to be the white coordinates. So this is gonna be X coordinate and there's gonna be a y coordinate in the inverse graph. Okay, So when you flip the coordinates of the grafted that into question, you're gonna get the inverse graphs. So when you do that, your inverse, the universe craft you're gonna get is going to look something like Yes, I'm not good at drawing something like this, right? So that is what your universe graph is gonna be. It's gonna look like. And now you want to find F inverse prime of three. Use this relation F F inverse of three. This is the same as that, right? Because there is no F. Prime. So, what you have is just the F. And the F universe. Right? So, using this graph, find F universe of three. And then using the graph in the question fine F of the resulting whenever you do that, you didn't see that you're just gonna have one half as the as the universe, the universe, the universe crime, right? You're gonna have uh negative one half. Yeah, so negative one half as the universe. The as the derivative of the universe at X equals three.

So given the graph, you want to find the universe graph, Right? So like I said, once again, for example, if I have a graph like this and this is a point two. Common one means that whenever X. Is to why? Here is one. So this is a point. This is a point on the graph. If I want to sketch the universe craft, then it's not gonna just gonna swap. Right? Let me put the members graph in a different color. Different. You have to swap. This one says the universe graph on the inverse graph to come along is going to be one to come with you. Okay? So it means that this is gonna be one and this is not gonna be too. So you can see that it's gonna turn into something like this. And then this is one coming to so many points on a coordinate, any point on the on the curve of the function itself. It's gonna be a swamp of a point. The gate on the universe curve. That is how you draw the universe graph from a given graph. Okay, so if you follow this one, you can see that the immigrants craft you're gonna get from the graph. Given the question is going to be it's going to look something like this, right? It is not drawn to scale but it's going to look something like this. Mm uh you know, something like this. Yeah, Okay. It's going to do something like that. So that is how your graph is going to be. You're in first graph. So this is F immersive X. Given the graph in the question. Okay, just swap the the coordinates. I swap, swap like three of them and then rule a line through, through and then that's it, Right, swap the coordinates. And then really lying through. Just swap like three. And then just put a line through and you're gonna get the interest graph. Now you want to find F inverse prime of X. And you're gonna use this relation One over f of f. Universal three. So first use the inverse graph To find f in front of three. Whatever the result is going to be, then fine F of that result in the original graph. And you're gonna see that this is going to be yeah, -1 3rd, approx. Right? It's going to be negative. So approximately is gonna be negative 1/3. Uh huh.


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