Question

if the parent function is y=1/x describe the changes in the equation y=3/x+1-2..
A) Vertical stretch by a factor of |3|, moves 1 unit to the right, moves down 2 units

B)Vertical stretch by a factor of |3|, moves 1 unit to the left, moves down 2 units

C) Vertical stretch by a factor of |3|, moves 1 unit to the right, moves up 2 units

D) vertical stretch by a factor of |3|, moves 1 unit to the left, moves up 2 units

Answer 1

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

\begin{array}{llll}

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

\begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array}
\\

% template start
\qquad \downarrow\qquad\qquad\quad\ \downarrow\\
y = {\color{purple}{ A}} ( x + {\color{red}{ C}} ) + {\color{green}{ D}}\\
%template end
\qquad\qquad \quad \uparrow \\

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

\begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array}
\end{array}
\\ \quad \\
\textit{or if you wish, it's also }\implies y=\cfrac{{\color{purple}{ A}}}{x+{\color{red}{ C}}}+{\color{green}{ D}}
}\)

Answer 2

the C component, applies to where the "x" may be encased