the function $f(x)=2^{x}$ is translated left 3 units and down 2 units. which is the equation of the…

Explanation:

Step1: Recall horizontal - translation rule

For a function $y = f(x)$, a left - shift of $h$ units gives $y=f(x + h)$. Here, $h = 3$ and $f(x)=2^{x}$, so after a left - shift of 3 units, the function becomes $y = 2^{x+3}$.

Step2: Recall vertical - translation rule

For a function $y = f(x)$, a down - shift of $k$ units gives $y=f(x)-k$. Here, $k = 2$, so after a down - shift of 2 units from $y = 2^{x + 3}$, the function becomes $g(x)=2^{x+3}-2$.

Answer:

D. $g(x)=2^{x + 3}-2$