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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 :)

Respuesta :

we are given

[tex]f(x)=\frac{3x-1}{x+4}[/tex]

(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

[tex]x+4=0[/tex]

[tex]x=-4[/tex]............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

[tex]y=f(x)+c[/tex]

now, we have

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

so, we can write our function as

[tex]g(x)=f(x)+4[/tex]

we can plug f(x)

[tex]g(x)=\frac{3x-1}{x+4}+4[/tex]

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

[tex]g(x)=\frac{3x-1}{x+4}+4=8[/tex]

Multiply both sides by x+4

[tex]\frac{3x-1}{x+4}\left(x+4\right)+4\left(x+4\right)=8\left(x+4\right)[/tex]

[tex]3x-1+4\left(x+4\right)=8\left(x+4\right)[/tex]

[tex]7x+15=8x+32[/tex]

[tex]7x=8x+17[/tex]

[tex]-x=17[/tex]

[tex]x=-17[/tex]..............Answer

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