Answer:
Option (d).
Step-by-step explanation:
Note: The base of log is missing in h(x).
Consider the given functions are
[tex]h(x)=\log_2x[/tex]
[tex]m(x)=\log_2(x+3)[/tex]
The function m(x) can be written as
[tex]m(x)=h(x+3)[/tex] ...(1)
The translation is defined as
[tex]m(x)=h(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.
On comparing (1) and (2), we get
[tex]a=3,b=0[/tex]
Therefore, we have to translate each point of the graph of h(x) 3 units left to get the graph of m(x).
Hence, option (d) is correct.
