Answer
$a.$
Since $g(x)=-f(x)+1$, we start with the graph of f(x) and
- reflect it about the x-axis ... to get $-f(x)$,
- and raise it up by $1$ unit ... to get $-f(x)+1$.
$b.$
Since $g(x)=f(-x)+1$, we start with the graph of f(x) and
- reflect it about the $y$-axis ... to get $f(-x)$,
- and raise it up by $1$ unit ... to get $f(-x)+1$.
Work Step by Step
The exercise is to describe transformations,
so the answer is given in step-by-step form.
