Question

if g(x) is a horizontal translation 6 units right of f(x)=x-2, what is the rule for g(x)?

Answer 1

\(\large
{\textit{function transformations}
\\ \quad \\

\begin{array}{llll}

\begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\cdot {\color{blue}{ B}}\end{array}
\qquad
\begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array}

\begin{array}{llll}{\color{green}{ D}} > 0& Up\\ {\color{green}{ D}} < 0 & Down\end{array}
\\

\qquad \downarrow\qquad\qquad\quad \downarrow\\
y = {\color{purple}{ A}} ( {\color{blue}{ B}}x + {\color{red}{ C}} ) + {\color{green}{ D}}\impliedby f(x)\\
\qquad\qquad\uparrow \\

\qquad\begin{array}{llll} horizontal\\ shift\\ by \ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}}\end{array}

\begin{array}{llll}\frac{{\color{red}{ C}}}{{\color{blue}{ B}}} > 0 & to \ left\\ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}} < 0& to \ right\end{array}

\end{array}
}\) any ideas?