Question

Which answer describes the transformation of f(x)=log2(x−5)−2 from the parent function g(x)=log2x ?

Answer 1

Which answer describes the transformation of  $f(x)=log_{2} (x-5)-2$ from the parent function $g(x)=log_{2} x$ 

D. It is the graph of $g(x)$ shifted 5 units right and 2 units down.

Answer 2

Applying translation concepts, it is found that the correct option is:

It is the graph of g(x) shifted 2 units down and 5 units right.

The original function is:

$g(x) = \log_2{x}$

The modified function is:

$f(x) = \log_2{(x - 5)} - 2$

• We have that when a function g(x) is shifted a units to the right, the equivalent function is g(x - a), hence, in this problem, since $\log_2{x} \rightarrow \log_{2}{(x - 5)}$, the function was shifted 5 units right.

• 2 was also subtracted from the original function, which means that it was shifted down 2 units.

A similar problem is given at https://brainly.com/question/18405655