Question

Question 13 plz show ALL STEPS

Answer 1

Explanation:

Here are some of the graphs:

Blue is g(x) and Green is f(x). The 2nd graph is for the 13b. It shows our graph after 1 transformation. The 3rd graph is after both transformations.

13a. Let use the following values in

`f(x) = (2)/(x)`

We know by definition of rational function x cannot be zero.

Let find some values across interval 2 through 4.

`f(2) = (2)/(2) = 1`

`f(3) = (2)/(3)`

`f(4) = (2)/(4) = (1)/(2)`

Let use the following values in

`g(x) = (3x - 1)/(x - 1)`

By definition of rational function, x cannot be 1 because it will make the denominator zero. Let use some values across the interval 0 through 4.

`g(0) = (0 - 1)/(0 - 1) = 1`

`g(2) = (3(2) - 1)/(2 - 1) = {5}`

`g(3) = (8)/(2) = 4`

`g(4) = (11)/(3)`

So graph this in a table of values. I'll post a picture of the table of values on the top.

13b. We need to write g(x) as a transformation of f(x). If we look at the graphs, g(x) has a asymptote at x=1 while f(x) has a asymptote of 0. This means that we need to move f(x) to the right one unit or move (x-1) units.

We will upgrade the graph.

Now we can just add 3 to f(x) to get to g(x).

In the 3rd graph, notice how both graphs coincide. Our transformations is complete.

The answer is

`g(x) = f(x - 1) + 3`

13c. We can say this as we move f(x) to the right 1 unit and shift f(x) up 3 units.