Transform the graph of $f\left(x\right)$ so that the transformed graph overlaps with the light colored graphs above.
The black graph shows the example $f\left(x\right)\rightarrow f\left(x-3\right)+4$.
blue graph$\color{#2d70b3}{\quad f\left(x\right)\rightarrow}$
$f\left(x\right)$ has been
by vector
$\bigg($
$\bigg)$
green graph$\color{#388c46}{\;\, f\left(x\right)\rightarrow}$
$f\left(x\right)$ has been
by vector
$\bigg($
$\bigg)$
red graph$\color{#c74440}{\quad f\left(x\right)\rightarrow}$
$f\left(x\right)$ has been
by vector
$\bigg($
$\bigg)$
Transform the graph of $f\left(x\right)$ so that the transformed graph overlaps with the light colored graphs above.
The black graph shows the example $f\left(x\right)\rightarrow f\left(x-3\right)+4$.
blue graph$\color{#2d70b3}{\quad f\left(x\right)\rightarrow}$
$f\left(x\right)$ has been
by vector
$\bigg($
$\bigg)$
green graph$\color{#388c46}{\;\, f\left(x\right)\rightarrow}$
$f\left(x\right)$ has been
by vector
$\bigg($
$\bigg)$
red graph$\color{#c74440}{\quad f\left(x\right)\rightarrow}$
$f\left(x\right)$ has been
by vector
$\bigg($
$\bigg)$
The equation of $f\left(x\right)$ above is $f\left(x\right)=\sqrt{x}$.
$f\left(x\right)=\sqrt{x}\quad\xrightarrow{\text{translated by }\binom{3}{4}}\quad f\left(x-3\right)+4=\sqrt{x-3}+4$.
Find the equations of the other graphs in terms of $x$.
$\color{#2d70b3}{f\left(x-2\right)-6=}$
$\color{#388c46}{f\left(x+5\right)-4=}$
$\color{#c74440}{f\left(x+8\right)=}$
The graph of $f\left(x\right)=e^x$ is translated by the vector $\displaystyle{\binom{-4}{-1}}$ to form $g\left(x\right)$. Find the equation of $g\left(x\right)$.
The graph of $f\left(x\right)=x^2$ is translated by the vector $\displaystyle{\binom{3}{2}}$ to form $g\left(x\right)$. Find the equation of $g\left(x\right)$ in the form $ax^2+bx+c$ where $a,b,c\in \mathbb{Z}$
The graph of $f\left(x\right)=x^2-x$ is translated by the vector $\displaystyle{\binom{3}{2}}$ to form $g\left(x\right)$. Find the equation of $g\left(x\right)$ in the form $ax^2+bx+c$ where $a,b,c\in \mathbb{Z}$
The graph of $f\displaystyle{\left(x\right)=\frac{1}{2x}}$ is translated by the vector $\displaystyle{\binom{-2}{3}}$ to form $g\left(x\right)$. Find the equation of $g\left(x\right)$ in the form $\displaystyle{\frac{ax+b}{cx+d}}$ where $a,b,c,d\in \mathbb{Z}$