Answer: Third option.
Step-by-step explanation:
Some transformations for a function f(x) are shown below:
If [tex]f(x)+k[/tex], the function is translated "k" units up
If [tex]f(x)-k[/tex], the function is translated "k" units down.
If [tex]f(x+k)[/tex], the function is translated "k" units left.
If [tex]f(x-k)[/tex], the function is translated "k" units right.
In this case you have the following function:
[tex]f(x)=3x+2[/tex]
And you know that the function g(x) is obtained by translating the function f(x) 5 units down and 3 units left; therefore, you can conclude that g(x) is:
[tex]g(x)=3(x+3)-3[/tex]
Finally, simplifying, you get that this is:
[tex]g(x)=3x+9-3\\\\g(x)=3x+6[/tex]
