Answer:
3 unit left and 2 unit up.
Step-by-step explanation:
Given : [tex]f(x)= \log_2(x + 3)+2[/tex] as a transformation of the graph of [tex]g(x) = \log_2x[/tex]
To find : Which best describes the graph transformation?
Solution :
The parent function [tex]g(x)=\log_2x[/tex]
with the vertex (1,0)
And the graph of [tex]f(x)=\log_2(x + 3)+2[/tex]
with the vertex (-2.75,0)
The graph of f(x) is the translation of g(x)
Transformation to the left,
f(x)→f(x+b) , the graph of f(x) is shifted towards left by b unit.
Same as the graph g(x) is shifted towards left by 3 unit and form graph of f(x).
[tex]f(x)= \log_2(x + 3)[/tex]
Transformation towards up,
f(x)→f(x)+a , the graph of f(x) is shifted upward by a unit.
Same as the graph g(x) is shifted upward by 2 unit and form graph of f(x).
[tex]f(x)= \log_2(x + 3)+2[/tex]
Therefore, The description of the transformation is 3 unit left and 2 unit up.
Refer the attached graph below.
