Question

two functions are given below.
$f(x) = \log_{2}x$
$g(x) = \log_{2}(x + 3)$
which transformation can be applied to the graph of $f(x)$ to obtain the graph of $g(x)$?
translate the graph of $f(x)$ 2 units to the left.
translate the graph of $f(x)$ 2 units to the right.
translate the graph of $f(x)$ 3 units to the left.
translate the graph of $f(x)$ 3 units to the right.

Explanation:

Step1: Recall horizontal shift rule

For a function $f(x)$, $f(x + a)$ (where $a>0$) shifts the graph of $f(x)$ left by $a$ units.

Step2: Match to given functions

Here, $g(x) = f(x + 3)$ where $f(x)=\log_2 x$ and $g(x)=\log_2(x+3)$.

Answer:

Translate the graph of $f(x)$ 3 units to the left.