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