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What quantitics did vOu graph on ycur horizontal and verticalE=€27 1 &Sonnb 0 / 10What is Ue relalionship ULlveen tle distante betwecothe spheres? What is...

Question

What quantitics did vOu graph on ycur horizontal and verticalE=€27 1 &Sonnb 0 / 10What is Ue relalionship ULlveen tle distante betwecothe spheres? What is YoUr evidence?{ W2 22Sobm_= 0 / 10

What quantitics did vOu graph on ycur horizontal and vertical E=€2 7 1 & Sonnb 0 / 10 What is Ue relalionship ULlveen tle distante betweco the spheres? What is YoUr evidence? { W 2 22 Sobm_= 0 / 10



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Graph the polynomials $P(x)=3 x^{5}-5 x^{3}+2 x$ and $Q(x)=3 x^{5}$ on the same screen, first using the viewing rectangle $[-2,2]$ by $[-2,2]$ and then changing to $[-10,10]$ by $[-10,000,10,000] .$ What do you observe from these graphs?

You're asked to plot the function Weigel, Synnex and Graphing Calculator and three windows. Basically, the first one you're going to start up here would be the negative 222 interval for your X and Y limits. And then you're just going to zoom in. So you know, this one will be the negative 1 to 1 interval for both X and Y, and this will be the negative 0.5 0.5 rule. And then you're asked to to say what you notice about what's happening as you zoom in. Well, if we're looking at a point as the focus right, it would be the very center. So 00 And as you zoom in, you notice that this curve starts to straighten out a little bit. Until here, you almost have a straight line through that point, and that would be essentially the tangent line. So So as you zoom and the curve becomes mhm indistinguishable from the tangent line at the center, Yeah, so essentially, you're seeing the slope at the very middle point, and then the function is starting to just resemble a straight line. It's almost impossible. You can kind of see little bit of curve there and there, but as you get him further, just will be a straight line

Okay here we have the craft of Y equals E. To the X. And we want to make some observations about the appearance of the graph as we zoom into the 0.0 comma one, the 0.0 common one, X zero Y. It was one, is this point right on the graph. So right now we would observe that white was E. T. X. Is an increasing function. Uh It's positive. Um And you know, informally we could say it's kind of bending or curving up. If we start to zoom in a little bit, We would still say looking at this .001, we would still say of course it's positive. It's still kind of curbing up. And as we continue to zoom in, I pay attention to this curve. Yeah. All right. Here's 2.0 comma one. Obviously the entire function is still positive and curving up. But notice how, you know now that we're really zooming in. Notice how it seems to flatten out a little bit if we zoom in a little bit more. All right. Now, if you look at the point as Euro comma one, you can see that it's really starting to flatten out. So when we were zoomed out, you could tell that this function was curving upwards. But as we zoom in closer and closer to the 0.0 comma one, the curve appears to flatten out. It's not really flat. You know, it's curving up but it appears to flatten out, resuming one more time. You can see that it almost gives you the mistaken impression that it's a straight line, which of course it's not. Um but as you zoom in, the current really does start to flatten out okay.

So here we have you to the X on the interval. Negative 1 to 1. Presuming Sorry. We zoom in, get it a little Flatter the reason that further You're gonna be flattered. Expected to happen continuously.

Okay, so for this problem we are going to be graphing X squared. Okay. Plus why minus one squared is equal to nine. Um If you want to check for symmetries, you can plug in negative X and see if you get the exact same function. So if I plug in negative X. And I don't change anything else about this problem. While negative X squared is the same thing as positive X squared. So if I plug in negative X, I get the same as if I plugged in positive X. So that means this is symmetric about the y axis. So it's got y axis symmetry. Um And then to check for X axis symmetry, I can plug in negative why and see if I get the exact same um function. And I could factor out a negative here and get Y plus one. And then if I square that then the negative one goes away and I get positive why again? But it still changes it to be positive Y plus one instead of y minus one. So this is not symmetric about the X axis. So this will only be symmetric about the y axis. Um And then to find X and Y intercepts, I can plug in, X equals zero and Y equals zero. So let's start with X intercepts, plug in, Y equals zero. You get x squared plus uh negative one squared is equal to nine, then I could subtract one from both sides. You get X squared is equal to eight. Take the square root, you get X. X equals plus or minus route eight which is a little bit less than three. Um And then to find y intercepts were going to plug in X equals zero, so zero plus y minus one squared is equal to nine. Take the square root of both sides. You get y minus one equals plus or minus Route nine which is three, add one to both sides. You get, Y is equal to one, plus, three is four and one minus three is negative two. So let's go ahead and start plotting we have Y equals four and negative two. For my Y intercepts, my X intercepts are plus or minus route eight, so it's a little bit less than three and negative three. Um And this is actually an ellipse and this ellipsis centered at 01 Um Actually you know what, it's not on the lips, it's a circle that Senator 01 because this is simply a transformation of the parent function X squared plus Y squared equals r squared. So this is a circle with a radius of three and um it is just shifted up one unit. So our center is located here and then from there we can go up three sideways three down three. Um And then our circle looks like this


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