Question

find g(x), where g(x) is the translation 9 units right of $f(x) = -10(x + 2)^3 + 8$.
write your answer in the form $a(x - h)^3 + k$, where $a$, $h$, and $k$ are integers.
$g(x) = $

Explanation:

Step1: Recall translation rule

For a function \( y = f(x) \), translating it \( h \) units right gives \( y = f(x - h) \).

Step2: Apply the rule to \( f(x) \)

Given \( f(x)=-10(x + 2)^{3}+8 \), translating 9 units right means replace \( x \) with \( x - 9 \) in \( f(x) \).
So \( g(x)=f(x - 9)=-10((x - 9)+ 2)^{3}+8 \).

Step3: Simplify the expression

Simplify \( (x - 9)+ 2=x - 7 \).
Thus, \( g(x)=-10(x - 7)^{3}+8 \).

Answer:

\( g(x)=-10(x - 7)^{3}+8 \)