Question

use the image to answer the question.
$f(x)=\log_{2}x$
$g(x)=\log_{2}x-3$
describe the transformation that occurred to the parent logarithmic function. (the parent function is in red.)
(5 points)
○ a vertical shrink by $\frac{1}{2}$
○ a shift down 3 units
○ a reflection over the x-axis
○ a shift up 3 units

Explanation:

For a parent function $f(x)$, the transformation $f(x) - k$ results in a vertical shift of the parent graph downward by $k$ units. Here, $g(x) = \log_2 x - 3 = f(x) - 3$, so the parent graph is shifted down 3 units, which matches the visual difference between the red and dotted curves.

Answer:

a shift down 3 units