Question

What is the answer to the problem above in the picture

Answer 1

Answer: Third option.

Step-by-step explanation:

Some transformations for a function f(x) are shown below:

If $f(x)+k$, the function is translated "k" units up

If $f(x)-k$, the function is translated "k" units down.

If $f(x+k)$, the function is translated "k" units left.

If $f(x-k)$, the function is translated "k" units right.

In this case you have the following function:

$f(x)=3x+2$

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:

$g(x)=3(x+3)-3$

Finally, simplifying, you get that this is:

$g(x)=3x+9-3\\\\g(x)=3x+6$