Question

consider the function y=x^2+5x-2, what would happen to the graph of (x-3) was substituted in place of the x

Answer 1

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

what do you think?

Answer 2

bear in mind that the parent function for that one would be y = x
or y = 1 ( x + 0)+0
which is the same as y = x