Question

PLS HELP!! 15 points

Consider the following function: f(x) = 3x-1 / x+4
a) At which value of x will the function not have an answer? Explain.
b) If g(x) is a vertical shift of 4 units of 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.
thank u :)

Answer 1

we are given

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

(a)

We know that when denominator of any function is 0

then function will become undefined

so, denominator=0 will make function no solution

so, we set denominator =0

and then we solve for x

`x+4=0`

`x=-4`............Answer

(b)

Vertical shift:

Suppose, we want to shift y=f(x) function vertically by 'c' units

we add 'c' top y-value

so, new function will become

`y=f(x)+c`

now, we have

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

so, we can write our function as

`g(x)=f(x)+4`

we can plug f(x)

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

Comparison:

So, graph of f(x) is moved upside by 4 units to get graph of g(x)

(c)

We can set g(x)=8

and then we can solve for x

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

Multiply both sides by x+4

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

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

`7x+15=8x+32`

`7x=8x+17`

`-x=17`

`x=-17`..............Answer