Question

g is related to one of the parent functions. Describe the sequence of transformations from f to g. g(x) = -x^3 - 1

Transformations of functions

g is related to one of the parent functions. Describe the sequence of transformations from f to g. $$g(x) = -x^3 - 1$$

We are starting with the parent function $$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}$$
STEP 1: Reflect the graph across x-axis, to get $$\displaystyle{y}=-{x}^{{3}}$$
STEP 2: Shift the graph by 1 unit down, to get $$\displaystyle{y}=-{x}^{{3}}-{1}$$, which is the required function g(x)