# Transformation geometry questions and answers

Recent questions in Performing transformations
Performing transformations

### $$f(x)= \frac{-1}{3(x+1)}+1$$ Domain and range? Transformations? Name of Graph?

Performing transformations

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

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

Performing transformations

### 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

### 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