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Given a series of transformations, find the new function

The graph of $f\left(x\right)$ (shown) is transformed in the following order:
  1. A reflection in the $x$-axis
    2. then
  2. A vertical dilation with scale factor $2$
    3. then
  3. A translation by vector $\binom{2}{0}$

In the Desmos window above, transform $f\left(x\right)$. Then write the final expression here:
The graph of $f\left(x\right)$ (shown) is transformed in the following order:
  1. A horizontal dilation with scale factor $2$
    2. then
  2. A translation by vector $\binom{0}{-3}$
    3. then
  3. A reflection in the $y$-axis

In the Desmos window above, transform $f\left(x\right)$. Then write the final expression here:
The graphs of both $\color{#2d70b3}{f\left(x\right)}$ and $\color{#c74440}{g\left(x\right)}$ are shown.
$\color{#2d70b3}{f\left(x\right)}$ is:
  1. Stretched vertically by scale factor 2
    2. then
  2. Translated vertically 1 unit up
In the Desmos window above, transform $\color{#2d70b3}{f\left(x\right)}$.
Then write the final expression here:
$\color{#c74440}{g\left(x\right)}$ is:
  1. Translated vertically 1 unit up
    2. then
  2. Stretched vertically by scale factor 2
In the Desmos window above, transform $\color{#c74440}{g\left(x\right)}$.
Then write the final expression here:
Explanation:
$f\left(x\right)\xrightarrow[\times 2]{\text{vert. stretch s.f. 2}} 2f\left(x\right)\xrightarrow[+1]{\text{vert. trans. up 1}}$
Explanation:
$g\left(x\right)\xrightarrow[+1]{\text{vert. trans. up 1}} g\left(x\right)+1\xrightarrow[\times 2]{\text{vert. stretch s.f. 2}}$
The graphs of both $\color{#2d70b3}{f\left(x\right)}$ and $\color{#c74440}{g\left(x\right)}$ are shown.
$\color{#2d70b3}{f\left(x\right)}$ is:
  1. Translated horizontally 1 unit to the left
    2. then
  2. Stretched horizontally by scale factor $\frac{1}{2}$
In the Desmos window above, transform $\color{#2d70b3}{f\left(x\right)}$.
Then write the final expression here:
$\color{#c74440}{g\left(x\right)}$ is:
  1. Stretched horizontally by scale factor $\frac{1}{2}$
    2. then
  2. Translated horizontally 1 unit to the left
In the Desmos window above, transform $\color{#c74440}{g\left(x\right)}$.
Then write the final expression here:
Explanation:
$f\left(x\right)\xrightarrow[x \,\Rightarrow \, x+1]{\text{hor. trans. left 1}} f\left(x+1\right)\xrightarrow[x \,\Rightarrow \, 2x]{\text{hor. stretch s.f.}\frac{1}{2}}$
Explanation:
$g\left(x\right)\xrightarrow[x \,\Rightarrow \, 2x]{\text{hor. stretch s.f.}\frac{1}{2}} g\left(2x\right)\xrightarrow[x \,\Rightarrow \, x+1]{\text{hor. trans. left 1}}$
The graph of $f\left(x\right)$ (shown) is transformed in the following order:
  1. Translated vertically 3 units down
    2. then
  2. Dilated vertically by scale factor $\frac{1}{3}$
    3. then
  3. Reflected about the $x$-axis
In the Desmos window above, transform $f\left(x\right)$. Then write the final expression here:
Explanation:
$f\left(x\right)\xrightarrow[-3]{\text{vert. trans. down 3}}$ $\xrightarrow[\times \frac{1}{3}]{\text{vert. dilate s.f.}\frac{1}{3}}$ $\xrightarrow[\times -1]{\text{reflect }x\text{-axis}}$
The graph of $f\left(x\right)$ (shown) is transformed in the following order:
  1. Dilated horizontally by scale factor 2
    2. then
  2. Reflected about the $y$-axis
    3. then
  3. Translated horizontally 2 units right
In the Desmos window above, transform $f\left(x\right)$. Then write the final expression here:
Explanation:
$f\left(x\right)\xrightarrow[x \,\Rightarrow \, \frac{1}{2}x]{\text{hor. dilate s.f.}2}$ $\xrightarrow[x \,\Rightarrow \, -x]{\text{reflect }y\text{-axis}}$ $\xrightarrow[x \,\Rightarrow \, x-2]{\text{hor. trans. right 2}}$