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Math Help - few questions about radical functions

  1. #1
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    few questions about radical functions

    the speed, s, in metres per secondm of sound in dry air can be described by the function s=331.3sqrt(1+T/273.15) T is degrees in celcius

    a) determine the domain and range of the function

    what i PUT:
    domain: {x|x>=-1,xer}
    range: {y|y>=0, yer}

    IT WAS WRONG
    geogebra said the x-int is 273.15 but i thought it would be -1 because it says +1 on the function and the range is apparently wrong too, anyways would be appreciated if someone helped.

    b) what is the meaninig of the x-intercept in this context?





    2. the manufacturer of a new GLOBAL POSITION SATELLITE system wants to predict the consumer interest in its new device. the company uses the function I(w)= -3sqrt(-w-1) +15 (square root is done after -1, +15 is alone) to model number, I, in thousandas, of pre-orders for the GPS as a function of the number ,w ,of weeks before the GPS release date.

    a) what are the domain and range and what do they mean in this situation?
    i put:
    domain: {x|x<=1,xer}
    range: {y|y<=15,xer}

    can u tell me if my answer is right and what do they mean in the situation




    b) identify the transformations represented by the function compared to y=sqrt(w)


    c)determine the number of pre-orders the manufacturer can expect to have 10 weeks before the release date?



    3. consider the function f(x)=2(x-1)^2-3
    a)determine square root of the function
    i put: g(x)=sqrt(2(x-1)^2-3 <--tell me if the square root is right

    and they told me to graph both equations and i cant seem to find the x-intercepts for the first function, if anyone can help.

    C)describe the relationship between the domain and range of f(x) and domain and range of g(x)





    (i know they seem alot, but i left most stuff out and the stuff i understood i left out. these questions are all too hard for me to do, if anyone can help, its test preparation and not cheating for homework, thnx if you help)
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: few questions about radical functions

    1.) We are given:

    s(T)=331.3\sqrt{1+\frac{T}{273.15}}

    To find the domain, we set:

    0\le1+\frac{T}{273.15}

    Now solve for T.

    Since the function is increasing as T increases, you will find the lower limit of the range by evaluating the function at the smallest value of T and the upper range is unbounded.

    Once we get this problem done and understood, I will move on the the next. I like to take them one at a time, and also solving this one will help you with the next one.
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    Re: few questions about radical functions

    Quote Originally Posted by MarkFL2 View Post
    1.) We are given:

    s(T)=331.3\sqrt{1+\frac{T}{273.15}}

    To find the domain, we set:

    0\le1+\frac{T}{273.15}

    Now solve for T.

    Since the function is increasing as T increases, you will find the lower limit of the range by evaluating the function at the smallest value of T and the upper range is unbounded.

    Once we get this problem done and understood, I will move on the the next. I like to take them one at a time, and also solving this one will help you with the next one.
    okay so i got the domain right, and as for the range, i got {y|y>=0,yer}...so it has to be above 0 because its a square root, did i get it right?
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    MHF Contributor MarkFL's Avatar
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    Re: few questions about radical functions

    A square root can be equal to zero, so your range is [0,∞). This is what you wrote using set-builder notation, but then you state it has to be above zero, so I just wanted to make it clear that it can include zero.

    I recommend using the variables given instead of converting the independent variable to x and the dependent variable to y.

    For 2a, your domain and range is correct if there were no other restrictions on I(w), but can we have a negative number of pre-orders?
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    Re: few questions about radical functions

    Quote Originally Posted by MarkFL2 View Post
    A square root can be equal to zero, so your range is [0,∞). This is what you wrote using set-builder notation, but then you state it has to be above zero, so I just wanted to make it clear that it can include zero.

    I recommend using the variables given instead of converting the independent variable to x and the dependent variable to y.

    For 2a, your domain and range is correct if there were no other restrictions on I(w), but can we have a negative number of pre-orders?
    no i put ">=" which includes 0 too i guess., and no negative number of pre-orders, i just need an answer sheet with explanation for the last few remaining questions, i dont know if u can be able to do them for me but i showed what i did on my own and i gotta go to bed now its like 2 am, could u be able to do the questions left and ill check in the morning?
    thank you for the help so far and thnx if u help with the rest.
    cya later mate.(edit: no we cant have negative pre-orders)
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: few questions about radical functions

    Actually, your domain is not right for 2a), you should have w\le-1.

    I cannot just finish your homework for you, but I am glad to help guide you.
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    Re: few questions about radical functions

    alright well thnx anyways gotta go
    Last edited by EASYPEAAZY; October 9th 2012 at 10:35 PM.
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: few questions about radical functions

    That sounds fine.
    Thanks from EASYPEAAZY
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