The geometric shape is a portion of a circle or a circular arc.

Question

asked 2021-02-03

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.

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.

asked 2020-11-22

Answer true or false to each of the following statements and explain your answers.

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.

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.

asked 2021-02-11

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.

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.

asked 2021-01-23

Sketch the graph of the function \(f(x) = -2^x+1 +3\) using transformations. Do not create a table of values and plot points

asked 2021-01-19

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.

\(y=sqrt(x - 2) - 1\)

\(y=sqrt(x - 2) - 1\)

asked 2021-01-08

Graph by labeling three points and determine the type or types of transformations:

\(h(x)=sqrt(x-2)-1\)

\(h(x)=sqrt(x-2)-1\)

asked 2021-02-05

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 =?

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 =?

asked 2021-01-15

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=?

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=?

asked 2020-11-27

Starting with the function \(f(x) = e^x\), create a new function by performing the following transformations.

i. First shift the graph of f (x) to the left by two units.

\(f_1 (x) =\)?

ii. Then compress your result by a factor of \(1/7\)

\(f_2 (x) =\) ?

iii. Next, reflect it across the x-axis.

\(f_3 (x) =\) ?

iv. And finally shift it up by eight units to create g (x).

g (x) =?

i. First shift the graph of f (x) to the left by two units.

\(f_1 (x) =\)?

ii. Then compress your result by a factor of \(1/7\)

\(f_2 (x) =\) ?

iii. Next, reflect it across the x-axis.

\(f_3 (x) =\) ?

iv. And finally shift it up by eight units to create g (x).

g (x) =?

asked 2020-10-27

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

\(A=[(1,-1),(-2,0)],B=[(1,5),(-2,0)]\)

\(A=[(1,-1),(-2,0)],B=[(1,5),(-2,0)]\)