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.

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+16=3x-1

4x-3x=-1-16

x=-17

Hence final answer is x=-17

Part a)

Part b)

Part c)

Step-by-step explanation:

we have

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

solve for x

Part b)  If g(x) is a vertical shift of 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

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

The function g(x) is equal to

Part c)  What is the value of x when ?

Substitute the value of in the equation and solve for x

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude