Answer
a) $f(x)=x^2$
b) Horizontal shift one unit to the right, reflection across the $x$-axis, vertical shift upward
c) See graph
d) $g(x)=-f(x-2)+4$
Work Step by Step
We are given the function:
$g(x)=4-(x-2)^2$
a) The parent function is:
$f(x)=x^2$
b) Horizontally shift $f(x)$ 2 units to the right to get $a(x)=(x-2)^2$.
Reflect $a(x)$ across the $x$-axis to get $b(x)=-(x-2)^2$.
Vertically shift $b(x)$ 4 units upward to get $g(x)=4-(x-2)^2$.
c) Graph the transformations:
d) Use function notation to write $g$ in terms of $f$:
$g(x)=-f(x-2)+4$
