Answer: last option.
Step-by-step explanation:
There are several transformations for a function f(x). Some of them are shown below:
1. If [tex]f(x)+k[/tex], then the function is translated "k" units up.
2. If [tex]f(x)-k[/tex], then the function is translated "k" units down.
3. If [tex]f(x+k)[/tex], then the function is translated "k" units left.
4. If [tex]f(x-k)[/tex], then the function is translated "k" units right.
In this case you have the following function:
[tex]h(x)=log_6x[/tex]
And the function m(x) is obtained by transformating the function h(x). This function is:
[tex]m(x)=log_6(x+3)[/tex]
Then, based on the transformatios shown before, you can identify that:
[tex]m(x)=h(x+3)[/tex]
Therefore, you can determine that you could graph the function [tex]m(x)=log_6(x+3)[/tex] by translating each point of the graph of the function h(x) 3 units left.
