Answer
a) $g(x)=x^3+1$
b) $g(x)=-(x+3)^3-1$
Work Step by Step
a) We start with the graph of the function $f(x)=x^3$.
Vertically shift $f(x)$ one unit upward to get the function from the given graph:
$g(x)=x^3+1$
b) We start with the graph of the function $f(x)=x^3$.
Reflect the graph of the function $f$ across the $x$-axis to get $a(x)=-x^3$.
Then horizontally shift $a(x)$ three units to the left to get $b(x)=-(x+3)^3$.
Finally, vertically shift $b(x)$ one unit downward to get the function from the given graph:
$g(x)=-(x+3)^3-1$
