Hurry! consider the function f(x)=3x-1 (over)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 from 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

Ans(a):

Given function is

we know that any rational function is not defined when denominator is 0 so that means denominator x+4 can't be 0

so let's solve

x+4≠0 for x

x≠0-4

x≠-4

Hence at x=4, function can't have solution.

Ans(b):

We know that vertical shift occurs when we add something on the right side of function so vertical shift by 4 units means add 4 to f(x)

so we get:

g(x)=f(x)+4

We may simplify this equation but that is not compulsory.

Comparision:  

Graph of g(x) will be just 4 unit upward than graph of f(x).

Ans(c):

To find value of x when g(x)=8, just plug g(x)=8 in previous equation

4x-3x=-1-16

x=-17

Hence final answer is x=-17

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