# Transformation geometry questions and answers Recent questions in Performing transformations
Performing transformations
ANSWERED ### $$f(x)= \frac{-1}{3(x+1)}+1$$ Domain and range? Transformations? Name of Graph?

Performing transformations
ANSWERED ### Let T $$\displaystyle{P}_{{2}}\rightarrow\mathbb{R}^{{3}}$$ be a transformation given by $$\displaystyle{T}{\left({f{{\left({x}\right)}}}\right)}={\left[\begin{array}{c} {f{{\left({0}\right)}}}\\{f{{\left({1}\right)}}}\\{2}{f{{\left({1}\right)}}}\end{array}\right]}$$ (a)Then show that T is a linear transformation. (b)Find and describe the kernel(null space) of T i.e Ker(T) and range of T. (c)Show that T is one-to-one.

Performing transformations
ANSWERED ### Functions f and g are graphed in the same rectangular coordinate system (see attached herewith). If g is obtained from f through a sequence of transformations, find an equation for g Performing transformations
ANSWERED ### List a sequence of transformations, in words, to convert the graph of $$f(x)=x^2$$ into the graph of $$g(x)=-6(x-2)^2+5$$.

Performing transformations
ANSWERED ### 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?

Performing transformations
ANSWERED ### Your friend attempted to describe the transformations applied to the graph of $$y=\sin x$$ to give the equation $$f(x)=\frac{1}{2} \sin(-\frac{1}{3}(x+30))+1$$. 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.

Performing transformations
ANSWERED ### 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: $$x=?$$ $$y =?$$

Performing transformations
ANSWERED ### Given $$f(x)=x2$$, after performing the following transformations: shift upward 58 units and shift 75 units to the right, the new function $$g(x)=$$

Performing transformations
ANSWERED ### 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.

Performing transformations
ANSWERED ### Given $$f(x)=x^2$$, after performing the following transformations: shift upward 52 units and shift 23 units to the right, write the new function g(x)=

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

Performing transformations
ANSWERED ### 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. $$y=\sqrt{x - 2} - 1$$

Performing transformations
ANSWERED ### Rectangle $ABCD$ABCD​ is translated and then reflected to create rectangle $A'B'C'D'$A′B′C′D′​ . Do rectangle $ABCD$ABCD​ and rectangle $A'B'C'D'$A′B′C′D′​ have the same area? Justify your answer.

Performing transformations
ANSWERED ### 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=?

Performing transformations
ANSWERED ### Area and Perimeter Formulas with Examples Area: — Total space enclosed by the boundary of a plane. Perimeter: — Length of the border around any enclosed plane.

Performing transformations
ANSWERED ### Graph by labeling three points and determine the type or types of transformations: $$h(x)=\sqrt{x-2}-1$$

Performing transformations
ANSWERED ### The measure of $$\angle DBE$$ is $$(0.1x - 22)^{\circ}$$ and the measure of $$\angle CBE$$ is $$(0.3x - 54)^{\circ}$$. Find the value of x.

Performing transformations
ANSWERED ### Explain how you could graph each function by applying transformations. (a) $$y = \log(x -2) + 7$$ (b) $$y = -3\log x$$ (c) $$y = \log(-3x)-5$$

Performing transformations
ANSWERED ### Determine the matrix representation of each of the following composite transformations. A pitch of $$90^{\circ}$$ followed by a yaw of $$90^{\circ}$$
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