# transformations

1. ### Polar co-ordinate transformations: Proof of x(dx/dt) + y(dy/dt) = r(dr/dt)

Standard transformation from Euclidean to Polar co-ordinates: x = rcos(@) and y = rsin(@) with r = radial distance from origin and @ the angle. Various problems I've come across state: x^2 + y^2 = r^2 which solves easily if you remember cos^2@ + sin^@ = 1, and then go on to state, x(dx/dt) +...
2. ### Having some trouble with combining functions in the form y=af(k(x-d))+c

Hi, This is my first attempt at getting some help on this website so I apologize if I did anything incorrectly. I recently started MRC3U Grade 11 University Prep Functions through an ILC course, and I've come across a question that has me stumped. We have to describe the transformations that...
3. ### Matrix representing composition of linear transformations

Could someone check these for me please and point out where needs improvement? Thanks in advance! \text{Prove that T is a linear transformation or show it isn't by use of a specific counter-example. If T is a linear transformation, find its associated matrix.} a.) T_{a} \begin{bmatrix}x \\...
4. ### Order For Transformations / Translations?

Hello, I am struggling with doing transformations and translations of the graphs of functions. Specifically I don't understand the order I am supposed to do them in. I have had to do problems where I am given the graph of a function and then I am asked to select the correct new graph based on...
5. ### Transformations of graphs

Question 1 The graph of the function y=e^x+10 is horizontally expanded by a factor of 6 and vertically expanded by a factor of 2. In terms of f(x) I know it would be y=2f(1/6x), but I am having problems plugging that into y=e^x+10. Question 2 The graph of the function y=x^3-7x is horizontally...
6. ### graph transformations

Hi; in f(x) = 3sqrt(x+2)-4 why does the 3 become before the square root when transforming the graph from its parent function? Thanks.
7. ### Linear Transformations

Hello everyone, I'm for days already on this question. Could someone please help me with it? I'm not asking for someone to do my homework, I really don't understand how to solve this and I tried a lot. It is a practice-exercise for which it would really help me to see the answer with seeing...
8. ### Conformal and non-conformal transformations

It is well known that from a two-dimensional solution of Laplace equation for a particular geometry, other solutions for other geometries can be obtained by making conformal transformations. Now, I have a function defined on a disc centered at the origin and is given by f(r) = a r where a is...
9. ### Linear Systems, stability, phase portraits and diagonal transformations

Hi everyone I'm taking a linear algebra class at university right now and this is one of my homework questions . I am unsure how to even approach this task and was looking for any pointers. I apologize in advance for not showing any attempt at this problem but I am completely stuck and don't...
10. ### List transformations of the graph.

Hi what are the transformations of a graph typically? My teacher gave me a picture of an graph in the first quadrant that is a parabola. The maximum point is positive, 9, so obviously it opens downwards. It is moved 3 to the right. Is there anything I am missing?
11. ### Using transformations to graph rational functions

Would someone explain what is happening to 1/(x+2). Seems it should've been (1/x)+2, I know that's not correct. What is loosing me on the algebra on this? Thanks, Joe
12. ### Change of Basis Matrix Transformations

Yo. So W is a subspace of C(-infinity, infinity) We have two different bases for W; B = {sin^2(x), cos^2(x)} B' = {2, 2*cos^2(x)-1} How do I find the transition matrix PB->B'​ ? This confuses me, because these bases are composed of functions and not vectors I'm not sure what technique to use to...
13. ### Need Help Figuring out Transformations of Quadratic Functions! (They're EVIL)

[Solved] Need Help Figuring out Transformations of Quadratic Functions! Hello, and thanks for reading my thread. So, Here's the problem: I'm taking an online math class (Secondary Math 2) and I'm very confused about transformations of quadratic functions. I have graphed the functions, but I...
14. ### Analysis of fouier transformations of the human heart beat

I'm doing a project on heart beat analysis for one of my math courses. I have attached an image of the graphs. I know the distance between heartbeats (shown by the blue line) indicates the time between each heart beat ( as indicated by the x-axis) I'm unsure of what the axis' for the Fourier...

16. ### Sum of Linear Transformations

Hello community. Here's something I haven't been able to prove: Let E be an n-dimensional vector space and f,g: E --- E be linear transformations such that f+g = e where e is the identity. If r(f)+r(g)= n (where r(f) denotes the rank of f), show that fof = f. I'd really appreciate any hints.
17. ### images under composite affine transformations

Hi I am looking for advice on how to tackle the following problem f and g are both affine transfomrations. the transformation f is rotation about (1-2) through -pi/2 , and the transformation g maps the points (0,0), to (1,0) and (0,1) to the points (2,2) (1,2) (2,1), respectively. find...
18. ### Which description matches the transformations y=cos x undergoes to produce y=3cos...

Which description matches the transformations y=cos x undergoes to produce y=3cos (-2x)? I am thinking that the answer is C. horizontal compression by factor 1/2, reflection through the y-axis, then vertical stretch by factor 3. I eliminated a. and d. because they deal with horizontal shifts...
19. ### Linear Transformations HELP.

So I'm given some homework problems and I'm pretty much stuck, and have no idea what I'm doing for all of them. 1. In each case assume that the transformations T is linear, and use theorem 2 to obtain the matrix A of T. Theorem 2 is: Let T: R^n -> R^m be a transformation. 1. T is linear iff...
20. ### All Linear Transformations where T = T^2

Let V be a vector space. Find all linear transformations T from V to V, where T = T2. I need help. Thanks.