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

Answer:

(A)

$x=-4$

(B)

$g(x)=\frac{3x-1}{x+4}+4$

(C)

$x=-17$

Step-by-step explanation:

we are given

$f(x)=\frac{3x-1}{x+4}$

(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

$g(x)=\frac{3x-1}{x+4}+4$

Graph:

(C)

we can set g(x)=8

and then we can solve for x

$8=\frac{3x-1}{x+4}+4$

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

$8x+32=7x+15$

$x=-17$