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artcher [175]
4 years ago
12

Consider the function f(x) = 3x-1/x+4.

Mathematics
2 answers:
andrew-mc [135]4 years ago
6 0

Ans(a):


Given function is f(x)=\frac{3x-1}{x+4}


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


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


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


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


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


4(x+4)=(3x-1)


4x+16=3x-1


4x-3x=-1-16


x=-17


Hence final answer is x=-17


Ne4ueva [31]4 years ago
4 0

Answer:

Part a) x=-4

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

Part c) x=-17

Step-by-step explanation:

we have

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

Part a) At which value of x will the function not have a solution?

we know that

In the function f(x) the denominator can not be zero

therefore

To find the value of x at which the function not have solution, equate the denominator to zero

x+4=0

solve for x

x=-4

Part 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)?

In this problem the rule of the translation f(x)-----> g(x) is

(x,y)------> (x,y+4)

That means-----> the translation is  4 units up

The function g(x) is equal to

g(x)=f(x)+4

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

Part c)  What is the value of x when g(x)= 8?

Substitute the value of g(x)= 8 in the equation and solve for x

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

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

4(x+4)=3x-1

4x+16=3x-1

4x-3x=-16-1

x=-17

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