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anonymous
 one year ago
f(x)=x^2(x1)(x+3)
Determine the end behavior: find the power function that the graph of f resembles for large values of x.
Find the xand yintercepts of the graph.
Determine whether the graph crosses or touches the xaxis at each xintercept.
anonymous
 one year ago
f(x)=x^2(x1)(x+3) Determine the end behavior: find the power function that the graph of f resembles for large values of x. Find the xand yintercepts of the graph. Determine whether the graph crosses or touches the xaxis at each xintercept.

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4look at the given polynomial f(x) whats the degree of f(x) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not given any additional information.. just was given the problem and asked to find that information..

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4Ahh, actually im asking you a question to see if you know how to find the "degree"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm pretty sure i understand how to find the x and y intercepts.. should i treat this as a normal polynomial function and cross multiply?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh!! i thought would be the exponent

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4it is indeed a polynomial, but do not multiply yet, i think we can finish the problem with out multiplying

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4yes, whats the degree of f(x) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i mean the degree is the exponent*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but then again I'm thinking its just 1

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4f(x)=x^2(x1)(x+3) notice that there are 3 factors here, multiplying them out gives the exponent of leading term as : 2+1+1 = 4 so the degree of f(x) is 4

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4for part a, the power function that the graph of f resembles for large values of x is \(\large x^4\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so as if i was to cross multiply id get an exponent of 2 for the first value and 1 and 1 on the middle and last term?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4Exactly! \(f(x)=\color{red}{x}^2(\color{red}{x}1)(\color{red}{x}+3)\) its easy to see that \(\color{Red}{x}^2*\color{Red}{x}*\color{red}{x}\) gives you \(\color{Red}{x}^{2+1+1} = \color{red}{x}^4\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what does finding the degree do for me though?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4good question, when you plugin large values of x, the function behaves almost same as the power function\(\large x^4\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I've been working similar problems and haven't needed that information to find the x and y intercepts

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4that degree thing helps in answering part a of question : `Determine the end behavior: find the power function that the graph of f resembles for large values of x.`

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4you can see here, how closely the graph of f(x) matches with the power function \(x^4\) https://www.desmos.com/calculator/vj2xhutn6z

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i havent been shown how to find the solution to these questions except for finding the x and y intercepts, domain/range, but not the power function.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok yes!! i see that now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so finding the degree will give me the power function..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry lot of questions... i think I'm just having a hard time understanding what I'm being asked to find.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4good, lets find the x intercepts

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so from what I've understood, to find the xintercept id want to find the value of the equation by f(x)=0, make the equation equal to 0, and finding the value of x.. thats why i assumed id cross multiply..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but now I'm not seeing how that would work.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4thats right! to find x intercepts, you want to solve \[\large x^2(x1)(x+3)=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is this problem similar to the problem f(x)={3+x If x<0 // x^2 if x> not equal to 0....

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4use zero product property to get : \(x^2=0\) or \(x1= 0\) or \(x+3=0\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4that gives you x intercepts : \(0, 1, 3\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0awesome!! ok so thats what i was thinking..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then id have to find the y intercept?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4yes, simply put \(x=0\) in f(x) to get the y intercepts

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4f(x)=x^2(x1)(x+3) f(0) = ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't i substitue all x values with 0?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4yes, but 3 is wrong

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4f(x)=x^2(x1)(x+3) f(0) = 0^2(01)(0+3) = ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4what do you get when u multiply something by 0 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cuz im retarded and looked at the problem as if the 0 in front of the parentheses was invisible lol...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4so the y intercept is 0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4how do we answer the last part `Determine whether the graph crosses or touches the xaxis at each xintercept.`

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0plot the points and read the graph and how it falls

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4look at the graph https://www.desmos.com/calculator/bdlowvla6f

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4notice that the graph is crossing x axis at x=3 and x=1 but it is just touching x axis at x=0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so it touches the x axis at 0,1,3 but only crosses at 1 and 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooh you answered before i could finish typing.. but that is what i saw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but then how do know the shape of the graph just by the points.. how do we know how far up it goes and where it lies on the rest of the graph

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4the graph goes forever on both ends, it sinks down : dw:1440390580159:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4zoomout in that desmos link and see...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but what about the part that is between (0,0) and (1,0)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0never mind i think I'm just over analyzing what i know and the "whys" to everything.. thank you for your help... i was on the right track for some of it.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4its all good :) here is a question for you : whats the reason for the graph of f(x) to just touch the x axis at x=0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4dw:1440390931586:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4if you see, the graph is just touching the x axis at x=0, it is NOT crossing the x axis

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Knowing, the xand yintercepts, the end behavior, the power function and where the graph is crossing and touching the xaxis at each xintercept... how should all of that be applied to graphing the equation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm supposed to label all intercepts and turning points... I understand that ill plot the (0,0), (1,0), (3,0) and label those as my xintercepts.. but i confused about how to label the turning points and how the power function is used.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1the turning points happen where the function has 0 slope

dan815
 one year ago
Best ResponseYou've already chosen the best response.1f(x)=x^2(x1)(x+3) you have to solve the equation d/dx(f(x)) =0 find d/dx(f(x)) and set to 0 and find at what x that happens

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know where the turning points occur.. I've already found the answers to everything.. the only thing I'm unsure about is how exactly is a turning point to be labeled on a graph and if and how a power function is to be labeled

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you put a point where u calculating the turning point for example(0,0) is a turning point

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is there a way to send you what I've written down and graphed?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1take a picture and attach file on here

dan815
 one year ago
Best ResponseYou've already chosen the best response.1or click on draw and roughly draw what u have
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