use the image to answer the question.\n$f(x)=\\log_{2}x$\n$g(x)=\\log_{2}x-3$\ndescribe the transformation…

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

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

Answer

Brief Explanations:

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