Question

In what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted? (1 point) Down 2, left pi over 2 Down 2, right pi over 2 Up 2, left pi over 2 Up 2, right pi over 2

Answer 1

Up 2, right pi over 2

Explanation:

Answer 2

`\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\---------------------------------\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}`

`\bf \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }(C)/(B)\\ ~~~~~~if\ (C)/(B)\textit{ is negative, to the right}\\\\`

`\bf ~~~~~~if\ (C)/(B)\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ ~~~~~~(2\pi )/(B)\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~(\pi )/(B)\ for\ tan(\theta),\ cot(\theta)`

so, with that template in mind,

`\bf f(x)=\stackrel{A}{-3}cos(\stackrel{B}{2}x\stackrel{C}{-\pi })\stackrel{D}{+2}~~ \begin{cases} C=-\pi \\ B=2\\ (C)/(B)=-(\pi )/(2)&\qquad \stackrel{\textit{horizontal shift}}{(\pi )/(2)\textit{ to the right}}\\[-0.5em] \hrulefill\\ D=+2&\qquad \stackrel{\textit{vertical shift}}{2\textit{ upwards}} \end{cases}`