## College Algebra (6th Edition)

$f(x)=|x|$ (Using desmos.com) we graph f(x) (blue dashed graph). By hand, plot the points (-2,2), (-1,1), (0,0), (1,1), (2,2) and the two rays which make the graph of f. $\mathrm{g}(x)=-2f(x+3)+2,$ so the graph of $g$ (solid red line) is obtained from the graph of f by 1. shifting it left by 3 units, then , 2. vertically stretching (factor 2) then , 3. reflecting across the x-axis (black, dashed line, and, finally, 4. raising up by 2 units (solid red line) Using the above points, $(x,f(x))$ plot $(x-3$, $-2f(x)+2)$ and join.