Answer
$a.$
Starting with the graph of $f(x)$,
- shift it to the left by 5 units ... to get $f(x+5)$ ,
- stretch it vertically by factor $2$... to get$ 2f(x+5)$ ,
- and lower it by 1 unit ... to get $2f(x+5)$.
$b.$
Starting with the graph of $f(x)$,
- shift it to the right by $3$ units ... to get $f(x-3)$
- compress it vertically by factor $\displaystyle \frac{1}{4}$... to get $\displaystyle \frac{1}{4}f(x-3)$ ,
- and raise it up by 5 units ... to get $\displaystyle \frac{1}{4}f(x-3)+5$
Work Step by Step
The exercise is to describe transformations,
so the answer is given in step-by-step form.