# Answer the questions and complete the following problems about transformations. 1. In a rotation of a set of points, what geometric structure defines the motion of points?

Question
Performing transformations
Answer the questions and complete the following problems about transformations. 1. In a rotation of a set of points, what geometric structure defines the motion of points?

2021-02-22
The geometric shape is a portion of a circle or a circular arc.

### Relevant Questions

Lily wants to define a transformation (or series of transformations) using only rotations, reflections or translations that takes Figure A to Figure B.

Which statement about the transformation that Lily wants to define is true?
A. It can be defined with two reflections.
B.It can be defined with one rotation and one translation.
C. It cannot be defined because Figure A and Figure B are not congruent.
D.It cannot be defined because the longest side of Figure B is on the bottom.
a. In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.
b. In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.
c. It is not always possible to fnd a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.
Your friend attempted to describe the transformations applied to the graph of $$y=sinx$$ to give the equation $$f(x)=1/2sin(-1/3(x+30))+1$$.
They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.
Sketch the graph of the function $$f(x) = -2^x+1 +3$$ using transformations. Do not create a table of values and plot points
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
$$y=sqrt(x - 2) - 1$$
Graph by labeling three points and determine the type or types of transformations:
$$h(x)=sqrt(x-2)-1$$
Create a new function in the form $$y = a(x- h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$
Give the coordinates of the vertex for the new parabola.
h(x) is f (x) shifted right 3 units, stretched by a factor of 9, and shifted up by 7 units. h(x) = ?
Edit Coordinates of the vertex for the new parabola are:
x=?
y =?
Create a new function in the form $$y = a(x-h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$.
Give the coordinates of the vertex for the new parabola.
g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?
Coordinates of the vertex for the new parabola are:
x=?
y=?
Starting with the function $$f(x) = e^x$$, create a new function by performing the following transformations.
$$f_1 (x) =$$?
ii. Then compress your result by a factor of $$1/7$$
$$f_2 (x) =$$ ?
$$f_3 (x) =$$ ?
In this problem, allow $$T1: RR2rightarrowRR2 and T2: RR2rightarrowR2$$ be linear transformations. Find $$Ker(T_1), Ker(T_2), Ker(T_3)$$ of the respective matrices
$$A=[(1,-1),(-2,0)],B=[(1,5),(-2,0)]$$