(50 points! ) consider the function f(x) = 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 of 4 units of f(x), write the function of 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.

we are given

(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

............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

now, we have

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

so, we can write our function as

we can plug f(x)

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

Multiply both sides by x+4

..............Answer

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step-by-step explanation: