Answer
a. compress horizontally by a factor of $\frac{1}{2}$, shift by $1$ unit downward
b. stretch horizontally by a factor of $2$, stretch vertically by a factor of $2$
Work Step by Step
$a.$
Starting with the graph of $f(x)$,
- compress it horizontally by a factor of $\frac{1}{2}$ ... to get $f(2x)$ ,
- and lower it by 1 unit ... to get $f(2x)-1$.
$b.$
Starting with the graph of $f(x)$,
- stretch it horizontally by a factor of $\displaystyle 2$... to get $f(\frac{1}{2}x)$ ,
- then stretch it vertically by a factor of $2$... to get $ 2f(\frac{1}{2}x)$.
