If you divide (6x +3) by (x +1) you get some quotient and some remainder. You can do it a variety of ways, including synthetic division and long division. The method used here is to rewrite 6x+3 as a multiple of x+1 with some constant term added.
.. 6x +3 = (6x +3) +3 -3
.. = (6x +3 +3) -3
.. = (6x +6) -3
.. = 6(x +1) -3
Now, you can divide this by (x +1) and you have
Then the boxes can be filled from ...
You know that
.. f(x) +6
represents a translation of f(x) by 6 units up
And you know that
.. f(x +1)
represents a translation of f(x) by 1 unit left
So, you can figure that
.. g(x) = f(x +1) +6
will represent a translation of 1 unit left and 6 units up of f(x) = -3/x.
.. 6x +3 = (6x +3) +3 -3
.. = (6x +3 +3) -3
.. = (6x +6) -3
.. = 6(x +1) -3
Now, you can divide this by (x +1) and you have
Then the boxes can be filled from ...
You know that
.. f(x) +6
represents a translation of f(x) by 6 units up
And you know that
.. f(x +1)
represents a translation of f(x) by 1 unit left
So, you can figure that
.. g(x) = f(x +1) +6
will represent a translation of 1 unit left and 6 units up of f(x) = -3/x.