Question

# g is related to one of the parent functions. Describe the sequence of transformations from f to g. g(x) = 2 - (x + 5)^2

Transformations of functions

g is related to one of the parent functions. Describe the sequence of transformations from f to g. $$g(x) = 2 - (x + 5)^2$$

$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}$$
$$\displaystyle{g{{\left({x}\right)}}}={2}-{\left({x}+{5}\right)}^{{2}}$$
$$\displaystyle{f}{1}{\left({x}\right)}={f{{\left({x}+{5}\right)}}}={\left({x}+{5}\right)}^{{2}}$$
$$\displaystyle{f}{2}{\left({x}\right)}={f}{1}{\left({x}\right)}=-{\left({x}+{5}\right)}^{{2}}$$
$$\displaystyle{g{{\left({x}\right)}}}={f}{2}{\left({x}\right)}+{2}=-{\left({\left({x}+{5}\right)}^{{2}}\right)}+{2}$$