which best describes the graph of $f(x)=log_2(x + 3)+2$ as a transformation of the graph of $g(x)=log_2x$?\n…

Explanation:

Step1: Recall transformation rules for functions

For a function $y = f(x - h)+k$, $h$ represents horizontal shift and $k$ represents vertical shift. If $h>0$, the graph shifts $h$ units to the right, if $h < 0$, the graph shifts $|h|$ units to the left. If $k>0$, the graph shifts $k$ units up. For the function $f(x)=\log_2(x + 3)+2$ compared to $g(x)=\log_2x$, we can rewrite $f(x)$ as $f(x)=\log_2(x-(- 3))+2$.

Step2: Determine horizontal and vertical shifts

Here, $h=-3$ and $k = 2$. Since $h=-3$, the graph of $g(x)$ shifts 3 units to the left. Since $k = 2$, the graph of $g(x)$ shifts 2 units up.

Answer:

a translation 3 units left and 2 units up