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How does changing the function from f(x) = –4 cos 3x to g(x) = –4 cos 3x – 6 affect the range of the function?
\(\bf f(x)=-4cos(3x)\qquad to\qquad g(x)=-4cos(3x)-6?\)
yes

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\(\large { f(x)=-4cos(3x)\qquad to\qquad g(x)=-4cos(3x){\color{green}{ -6}}\\ \textit{function transformations} \\ \quad \\ \begin{array}{llll} \begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array} \qquad \begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array} \begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array} \\ % template start \qquad \downarrow\qquad\qquad\quad\ \downarrow\\ y = {\color{purple}{ A}} ( x + {\color{red}{ C}} ) + {\color{green}{ D}}\\ %template end \qquad\qquad \quad \uparrow \\ \qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array} \begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array} \end{array} }\) what do you think?
one really easy thing to do in questions of this type is to graph both curves and observe the difference... it helps with understanding. this site will easily plot both curves https://www.desmos.com/calculator
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