Transformation Properties: Boost Your Knowledge

Recent questions in Transformation properties

CMIIh 2021-03-12

Complete the tasks to determine:
a)To graf: The function $g (x) = 2^{x - 4} .$
b)The domain of the function $g (x) = 2^{x - 4}$ in the interval notation.
c)The range of the function $g (x) = 2^{x - 4}$ in the interval notation.
d)The equation of the asymptote of the function $g (x) = 2^{x - 4} .$

aflacatn 2021-03-08

Describe how to obtain the graph of g and f if $g (x) = 2 (x + 2)^{2} - 3, h (x) = 2 x^{2}, a n d h (x) = 2 (x - 3)^{2} + 2$

Anish Buchanan 2021-03-07

To determine the solution of the initial value problem
$y^{″} + 4 y = \sin t + u_{π} (t) \sin (t - π) :$
$y (0) = 0,$
$y^{'} (0) = 0.$
Also, draw the graphs of the solution and of the forcing function and explain the relation between the solution and the forcing function..

Elleanor Mckenzie 2021-02-25

Prove these examples are correct:
a) What is the area of the largest rectangle that fits inside of the ellipse
$x^{2} + 2 y^{2} = 1 ?$
b) Prove the following: Let c in (a, b). If f is continuous on $[a, b],$ differentiable on (a, b)?

melodykap 2021-02-25

Provide answers to all tasks using the information provided.
a) Find the parent function f.
Given Information: $g (x) = - 2 | x - 1 | - 4$
b) Find the sequence of transformation from f to g.
Given information: $f (x) = [x]$
c) To sketch the graph of g.
Given information: $g (x) = - 2 | x - 1 | - 4$
d) To write g in terms of f.
Given information: $g (x) = - 2 | x - 1 | - 4 and f (x) = [x]$

CoormaBak9 2021-02-25

To calculate:
The reduced form of the provided matrix, $[\begin{matrix} 1 & 0 & - 3 & 1 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 3 & - 6 \end{matrix}]$ with the use of row operations.

Nann 2021-02-21

Which of the following are linear transformations from $R R^{2} \to R R^{2} ?$
(d) Rotation: if $x = r \cos θ, y = r \sin θ,$ then
$\vec{T} (x, y) = (r \cos (θ + φ), r \sin (θ + φ))$
for some constants $∠ φ$
(f) Reflection: given a fixed vector $\vec{r} = (a, b), \vec{T}$ maps each point to its reflection with
respect to $\vec{r} \vec{T} (\vec{x}) = \vec{x} - 2 {\vec{x}}_{r ⊥}$
$= 2 {\vec{x}}_{r} - \vec{x}$

Khaleesi Herbert 2021-02-19

(a) The new coordinates geometrically if X represents the point $(0, \sqrt{2})$ m and this
point is rotated about the origin $45^{\circ}$ clockwise and then translated 2 units to the right and 3 units upward.
(b) The value of $Y = A B X,$ and explain the result.
(c) If ABX equal to BAX. Interpret the resul.
(d) A matrix that translate Y back to X

Burhan Hopper 2021-02-12

To find: The Laplace transform of the function
$L {t^{4} - t^{2} - t + \sin \sqrt{2 t}}$

Ramsey 2021-02-11

Let $T : U \to U$ be a linear transformation and let beta be a basis of U Define the determinant det(T) of T as
det $(T) = d e t ([T]_{β}) .$
Show ta det (T) is well-defined, i. e. that it does not depend on the choice of the basis beta
Prove that T is invertible if and only if det $(T) \neq 0.$ If T is invertible, show that det $(T^{- 1}) = \frac{1}{d e t (T)}$

Jaden Easton 2021-02-08

a) Find the sequence of transformation from f to g
Given information: $g (x) = \frac{1}{2} | x - 2 | - 3 and f (x) = x^{3}$
b) To sketch the graph of g.
Given information: $f (x) = | x |$
c) To write g in terms of f.
Given information: $g (x) = \frac{1}{2} | x - 2 | - 3 and f (x) = | x |$

preprekomW 2021-02-03

To sketch:
(i) The properties,
(ii) Linear transformation.
Let $T : R^{2} \to R^{2}$ be the linear transformation that reflects each point through the
$x_{1} a x i s .$
Let $A = [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}]$

abondantQ 2021-01-22

The table shows some values of the derivative of an unknown function f.Complete the table by finding the derivative of each transformation of f, it possible
a) $g (x) = f (x) - 2$
b) $h (x) = 2 f (x)$
c) $r (x) = f (- 3 x)$

Caelan 2021-01-19

Show that mapping $y \mapsto r e f l_{L} y$ is a linear transformation.

facas9 2021-01-17

Guided Proof Let $v_{1}, v_{2}, . . . . V_{n}$ be a basis for a vector space V.
Prove that if a linear transformation $T : V \to V$ satisfies
$T (v_{i}) = 0 f o r i = 1, 2, . . ., n,$ then T is the zero transformation.
To prove that T is the zero transformation, you need to show that $T (v) = 0$ for every vector v in V.
(i) Let v be the arbitrary vector in V such that $v = c_{1} v_{1} + c_{2} v_{2} + \dots + c_{n} V_{n}$
(ii) Use the definition and properties of linear transformations to rewrite T(v) as a linear combination of $T (v_{j})$ .
(iii) Use the fact that $T (v_{j}) = 0$
to conclude that $T (v) = 0,$ making T the zero transformation.

FizeauV 2021-01-16

To determine the solution of the initial value problem
$y^{″} + 4 y = δ (t - π) - δ (t - 2 π), y (0) = 0, y^{'} (0) = 0$
and draw the graph of the solution.

glamrockqueen7 2021-01-10

Let T be a linear transformation from $P_{2} into P_{2}$ such that
$T (1) = x, T (x) = 1 + x and T (x^{2}) = 1 + x + x^{2} .$
Find $T (2 - 6 x + x^{2})$

Dottie Parra 2021-01-08

Prove that for all integers m, if even then $3 m + 5$ is odd.

Dottie Parra 2021-01-06

Draw a graph for each expression.
a) $f (x) = 2^{x}$
b) $f (x) = 2^{- x}$
c) $f (x) = - 2^{x}$
d) $f (x) = - 2^{- x}$

Emeli Hagan 2021-01-06

Determine if the statement is true or false.
For all real numbers a and b, if $a < b t h e n a < \frac{a + b}{2} < b .$

These integral calculations and transformation properties are always used in Jira, Python, Java, and many other types of applied programming when you need to apply 2D or 3D transformations of an object. When you need to work with the linear transformation properties by applying specific equations, you will find the collection of questions and answers helpful. When you need to provide graphical lab reports, make sure that you focus on the transformation properties as you design your assignment. Take a look at some examples to see the logic of how to write down transformations and explain the changes in motion.

Integral Calculus

Linear Transformation Properties: Expert Help & Solutions