Question

Consider the function fx=3x-1/x+4.

(A) At which value of x will the function not have a solution? Explain your answer.
(B) If g(x) is a vertical shift up 4 units from f(x), write the function g(x). How does the graph of g(x) compare to the graph of f(x)? Explain the function you wrote.
(C) What is the value of x when g(x)=8? Show your work.

Answer 1

(A)

`x=-4`

(B)

`g(x)=(3x-1)/(x+4)+4`

(C)

`x=-17`

Explanation:

we are given

`f(x)=(3x-1)/(x+4)`

(a)

we know that

any function is undefined when denominator =0

so, we can set denominator =0

and then we can solve for x

`x+4=0`

`x=-4`

So, it does not have solution at
`x=-4`

(b)

If g(x) is a vertical shift up 4 units from f(x)

Whenever we shift vertically upward by 'a' units , we always add 'a' to y-value

so, we get

g(x)=f(x)+4

we get

`g(x)=(3x-1)/(x+4)+4`

Graph:

(C)

we can set g(x)=8

and then we can solve for x

`8=(3x-1)/(x+4)+4`

`8\left(x+4\right)=3x-1+4\left(x+4\right)`

`8x+32=7x+15`

`x=-17`