which equation represents the function $f(x)=(1.6)^x$ after it has been translated 5 units up and 9 units to…

Explanation:

Step1: Recall horizontal - translation rule

For a function $y = f(x)$, a translation $h$ units to the right gives $y=f(x - h)$. Here, $h = 9$ and $f(x)=(1.6)^x$, so after translating 9 units to the right, the function becomes $y=(1.6)^{x - 9}$.

Step2: Recall vertical - translation rule

For a function $y = f(x)$, a translation $k$ units up gives $y=f(x)+k$. Here, $k = 5$. So after translating the function from Step 1, 5 units up, the function becomes $g(x)=(1.6)^{x - 9}+5$.

Answer:

$g(x)=(1.6)^{x - 9}+5$ (corresponding to the third option)