Question 5 (2 points) Sued The function y COS k(zcan be used to model the graph below:0.5511/6Oublank #1 caue Khewvaluc or kOn blawk #2 SLale the vallue ord in ter...

1-2 Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

$\begin{array}{ll}{\text { (a) } y=\frac{x-6}{x+6}} & {\text { (b) } y=x+\frac{x^{2}}{\sqrt{x-1}}} \\ {\text { (c) } y=10^{x}} & {\text { (d) } y=x^{10}} \\ {\text { (e) } y=2 t^{6}+t^{4}-\pi} & {\text { (f) } y=\cos \theta+\sin \theta}\end{array}$

So now they want us to sketch the graph of this function. So one thing that I think often helps is to first graph it in. One of the dimensions are two of the dimensions. And then from there, extrapolate to the third. Because wouldn't it be nice if we didn't have this tea here? We just had co signed t sign t So X, Y and Z So we know in the EC Z plane. So actually, I'll just go ahead and sketch the XZ plane over here. We quickly So X Z Well, this is just going to be the unit circle. So this is co sign t zero sign teeth. So now if we add this extra dimension to it, Well, why is just making it increase out? So we can kind of think about it as as this is spiraling around in the XY plane is going to start going up and down the why access. So let's go ahead and draw are three dimensional shape now. So this is the X why and z direction. So remember, in this X Z plane, so right here is going to be strolling around and it's gonna be moving up and down the by access. All right, so let's just figure out what zero is. So we have an idea of where we're actually starting this. So we have our zero, so that's going to be 100 So we should be starting at, like, at this point, Let me go ahead and move out a little bit more, so we should be starting about here. And then we were to remember it should be rotating around like this because this is the way the unit circle rotates. So we should also rotate in that same direction here. So remember, this is where X is positive. Then it goes towards the positive Z access. So in this case, that means we're gonna want to rotate like this. And we're going to just keep on spiraling along the y axis as it becomes bigger and going like this here. And it should also rotate in the other direction as well as why becomes negative, so goes down and then starts going like that. And it should still be oriented in this same direction, going towards the positive Z access like that so that there would be a sketch of our

The problem given here 42. We want to display the graphs of why one equals cosine x. So we have cooked on X and then Y, n equals the sign, have X plus H minus the sine of X all over H. Um and we want to let h as we see as we let age good to infinity, it goes to zero. So as this value changes, we see that the sign graph changes but they appear to be the same right at about zero. So the closer it gets to zero, the closer these graphs we see, we'll end up getting to one another and that makes sense because um letting hb these smaller values, we end up getting closer and closer. So as this gets closer to zero, we see that there's very little difference in them. We could zoom in here and see there is very little difference in them, especially as we just keep increasing. All right, keep increasing its value and making it closer to zero. So it's going to be our final way of expressing that and understanding that as the limit it goes to zero, or as the limit of h goes to zero of this value. Right here, it gets closer and closer to the coastline of X. Graph, and that's how we can understand the derivative of this sine function.

On Today we're going to solve problem number 20 here. Given X equals, think and y equals and squared deep for zero Latina record duty Latino record toe bye bye to so the X equal to city Why equals times correctly for D equals zero? It could be one. Why will be zero 40 equals by by six x will be 1.2. Why will be pointed three for me equals by before actually be 1.4. Why will be one for? Because by by three it will people who I will be three. So this is the girl that reported But I plan my values If you want to meet, it will be one plus times square t Tyco's things square data. But because Times Square D and X equals 60 so exit squaring cause things quality learn plus right It was extra square y equals X squared minus one for 60 greater than or equal to one for zero less than a report to be the recall toe. Bye bye to the domain is respected for X greater than or equal to one. Thank you

Today we're going to solve problems on the 70 here. X equals 50 on the y equals panting the lies between zero lesson regularity Last recalls by by two So p Mexico City Why? Because 20 PICO zero Excellent basics. Throw one both times the Lazaro by basics it will be one pointed toe. It's 0.6 20 equals by before actually 1.4 and why it will be one when p equals bye bye. Three x will be too. Why will be one point. So the plot will be this one. If he didn't make it, we can right leg by the world Indira one plus Times Square data Because six square data It's obstruct ex ACOs 50 Bye equals Dante one plus Why square? Because excess quit X squared minus y squared equals one so it can be restricted such that it should be greater than or equal to one. Why should be written or equal to zero? Thank you