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