Answer
a) $g(x)=x^2-1$
b)$g(x)=-(x+1)^2+1$
Work Step by Step
a) We start with the graph of the function $f(x)=x^2$.
Vertically shift $f(x)$ one unit downward to get the function from the given graph:
$g(x)=x^2-1$
b) We start with the graph of the function $f(x)=x^2$.
Reflect the graph of the function $f$ across the $x$-axis to get $a(x)=-x^2$.
Then horizontally shift $a(x)$ one unit to the left to get $b(x)=-(x+1)^2$.
Finally, vertically shift $b(x)$ one unit upward to get the function from the given graph:
$g(x)=-(x+1)^2+1$
