1. anonymous

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

2. jdoe0001

$$\bf f(x)=-4cos(3x)\qquad to\qquad g(x)=-4cos(3x)-6?$$

3. anonymous

yes

4. jdoe0001

$$\large { f(x)=-4cos(3x)\qquad to\qquad g(x)=-4cos(3x){\color{green}{ -6}}\\ \textit{function transformations} \\ \quad \\ \begin{array}{llll} \begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array} \qquad \begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array} \begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array} \\ % template start \qquad \downarrow\qquad\qquad\quad\ \downarrow\\ y = {\color{purple}{ A}} ( x + {\color{red}{ C}} ) + {\color{green}{ D}}\\ %template end \qquad\qquad \quad \uparrow \\ \qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array} \begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array} \end{array} }$$ what do you think?

5. campbell_st

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

6. anonymous

i need the answer right now

7. jdoe0001

To see what is in front of one's nose needs a constant struggle. ~~ George Orwell, "In Front of Your Nose" ~~