MATH SOLVE

10 months ago

Q:
# Help please I don’t understand this math problem

Accepted Solution

A:

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

[tex]\frac{6x+3}{x+1} = \frac{6(x+1)-3}{x+1} = \frac{6(x+1)}{x+1} +\frac{-3}{x+1} = \frac{-3}{x+1}+6[/tex]

Then the boxes can be filled from ...

[tex]g(x)=\frac{6(x+1)+(-3)}{x+1}=\frac{-3}{x+1}+6[/tex]

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

[tex]\frac{6x+3}{x+1} = \frac{6(x+1)-3}{x+1} = \frac{6(x+1)}{x+1} +\frac{-3}{x+1} = \frac{-3}{x+1}+6[/tex]

Then the boxes can be filled from ...

[tex]g(x)=\frac{6(x+1)+(-3)}{x+1}=\frac{-3}{x+1}+6[/tex]

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.