Question

1. complete the following.

part a. describe the transformation of $f$ represented by $g$.
$f(x)=\log_{2}x$, $g(x)=\log_{2}(x + 2)-3$
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

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 shift left by 2 units.

Step2: Identify vertical transformation

The $-3$ outside the logarithm is a vertical shift down by 3 units.

Step3: Identify transformation type

There is no stretch/shrink, only shifts.

Answer:

The graph of $g$ is a horizontal shift 2 units left and vertical shift 3 units down of the graph of $f$.