## Algebra and Trigonometry 10th Edition

$f(x)=3|x|-3$
Since the graph follows the shape $f(x)=|x|$ we will start with that equation: $f(x)=|x|$ First notice the graph is shifted down 3 units. Up and down shifts are added to the right side of the equation. Up is positive and down is negative: $f(x)=|x|-3$ Second, notice the graph has been stretched vertically (by a factor of k) and will follow the below equation: $f(x)=k|x|-3$ Substitute (-2,3) into the above equation to solve for k: $3=k|-2|-3$ $2k=6$ $k=3$ So we get the final function: $f(x)=3|x|-3$