Question

What is the answer to the problem above in the picture

Answer 1

Answer: Third option.

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`