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Transformations of Functions

$f(x)\rightarrow f(x)+b$ $f(x)\rightarrow f(x-a)$ $f(x)\rightarrow pf(x)$ $f(x)\rightarrow f(qx)$ $f(x)\rightarrow -f(x)$ $f(x)\rightarrow f(-x)$ The Order of Transformations

Extension Problems

The graph of $\displaystyle f\left(x\right)=\frac{k}{2x}$ is translated $1$ unit in the $x$-direction and $-1$ unit in the $y$-direction. The equation of the graph following this transformation is $\displaystyle g\left(x\right)=\frac{-2x+6}{2x-2}$. Find the value of $k$.

$k=$

A parabola with equation $y=ax^2+bx+c$ is reflected about the $x$-axis. Both graphs are translated horizontally by 10 units but in opposite directions to become the graphs of $f\left(x\right)$ and $g\left(x\right)$, respectively.
Find the equation of $f\left(x\right)+g\left(x\right)$ in terms of $a,b,c$ and $x$.

Given the function $f\left(x\right)=\ln x$, describe the transformations needed to get the graph of $g\left(x\right)=\ln \left(4x^2+4x+1\right)$

Translate $f\left(x\right)$ to the left by units and up by units, then stretch vertically by a scale factor of .