Question

$f(x) = \log_{2}x$, $g(x) = \log_{2} (x + 2) - 3$
the graph of $g$ is a $square$ $square$ units $square$ and $square$ units $square$ of the graph of $f$.
options:
2, 3, 6, 7, 8
up, down, left, right
vertical shrink, vertical stretch, horizontal shrink, horizontal stretch
reflection, translation
$x$-axis, $y$-axis

Explanation:

Step1: Identify horizontal transformation

For $f(x)=\log_2 x$, $g(x)=\log_2(x+2)-3$ has $x$ replaced by $x+2$. This is a horizontal translation left.

Step2: Identify horizontal translation amount

The value added to $x$ is 2, so shift left 2 units.

Step3: Identify vertical transformation

The $-3$ outside the log is a vertical translation down.

Step4: Identify vertical translation amount

The subtracted value is 3, so shift down 3 units.

Answer:

1. translation
2. left
3. 2
4. down
5. 3

Full statement: The graph of $g$ is a translation 2 units left and 3 units down of the graph of $f$.