Question

If the graph of the function h defined by =hx+−4x23 is translated vertically downward by 9 units, it becomes the graph of a function f . Find the expression for fx

Answer 1

Hmmm I can't quite make it the h(x) function, look like $h(x)=4x^{23}$  dunno

however, a vertical transformation or shift of 9 units is just a -9
so hmm notice here
$\qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ \begin{array}{rllll} % left side templates f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}}\mathbb{R}^{{{ B}}x+{{ C}}}+{{ D}} \end{array}$

$\begin{array}{llll} % right side info \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\ \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\ \qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\ \bullet \textit{ vertical shift by }{{ D}}\\ \qquad if\ {{ D}}\textit{ is negative, downwards}\\ \qquad if\ {{ D}}\textit{ is positive, upwards} \end{array}$