Consider the transformations outlined below.

1. How is the graph of $f(x) =\frac { 1 } { x }$ transformed to obtain the graph of $g(x) =\frac { 1 } { x + 2 } – 3$?

   Hint (a):

   There will be a vertical shift and a horizontal shift.

   Answer (a):

   $f$ is translated $2$ units left and $3$ units down to obtain $g$.

2. How is the graph of $y = x^{2}$ transformed to obtain the graph of $y = –\left(x – 1\right)^{2} + 20$?

3. How is the graph of $y =|x|$ transformed to obtain the graph of $y = –3| x + 71|$?

   Answer (c):

   To get the second graph, the first graph is vertically stretched by factor of $3$, reflected across the $x$-axis, and translated left $71$ units.