Answer
a) $f(x)=x^3$
b) Horizontal shift one unit to the left and reflect across the $x$-axis
c) See graph
d) $g(x)=-f(x+1)$
Work Step by Step
We are given the function:
$g(x)=-(x+1)^3$
a) The parent function is:
$f(x)=x^3$
b) Horizontally shift $f(x)$ one unit to the left to get $a(x)=(x+1)^3$.
Reflect $a(x)$ across the $x$-axis to get $g(x)=-(x+1)^3$.
c) Graph the transformations:
d) Use function notation to write $g$ in terms of $f$:
$g(x)=-f(x+1)$
