Answer
a) $f(x)=[[x]]$
b) Reflection across the $x$-axis, vertical shift
c) See graph
d) $g(x)=-f(x)+1$
Work Step by Step
We are given the function:
$g(x)=-[[x]]+1$
a) The parent function is:
$f(x)=[[x]]$
b) Reflect $f(x)$ across the $x$-axis to get $a(x)=-[[x]]$.
Vertically shift $a(x)$ one unit upward to get $g(x)=-[[x]]+1$.
c) Graph the function $g$.
d) Use function notation to write $g$ in terms of $f$:
$g(x)=-f(x)+1$
