Answer:
Options C and D.
Step-by-step explanation:
The given functions are
[tex]f(x)=2^{x-6}+3[/tex]
[tex]g(x)=2^{x-3}+2[/tex]
We need to find the transformation from f(x) to g(x).
Now, write the function g(x) in the form of f(x).
[tex]g(x)=2^{x+3-3-3}+2+1-1[/tex]
[tex]g(x)=[2^{(x+3)-6}+3]-1[/tex]
[tex]g(x)=f(x+3)-1[/tex] ...(1)
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (2)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2), we get
[tex]a=3>0[/tex], so graph shifts 3 units left.
[tex]b=-1<0[/tex], so graph shifts 1 unit down.
Therefore, the correct options are C and D.
