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

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

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.

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: \(x=?\) \(y =?\)

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

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.

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: \(h(x)=\sqrt{x-2}-1\)

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.

Explain how you could graph each function by applying transformations. (a) \(y = \log(x -2) + 7\)

(b) \(y = -3\log x\)

(c) \(y = \log(-3x)-5\)

Determine the matrix representation of each of the following composite transformations. A pitch of \(90^{\circ}\) followed by a yaw of \(90^{\circ}\)