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Math Help - Function

  1. #1
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    Function

    Hey Guys I've got a slight problem regarding the following question. Im enrolling into a course next year and im having problems solving the practice examples.

    CAn you please help me

    [IMG]file:///C:/Temp/msohtmlclip1/01/clip_image002.jpg[/IMG]Function-q1.png
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  2. #2
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    Re: Function

    Quote Originally Posted by mikel03 View Post
    Hey Guys I've got a slight problem regarding the following question. Im enrolling into a course next year and im having problems solving the practice examples.

    CAn you please help me

    [IMG]file:///C:/Temp/msohtmlclip1/01/clip_image002.jpg[/IMG]Click image for larger version. 

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    And what are the problems you are having?
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  3. #3
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    Re: Function

    All of it. Please Help Thanks
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  4. #4
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    Re: Function

    Sorry but that's not good enough, you need to have at least tried something... Do you understand what a function is (inputting numbers into a rule and getting a number out)? Do you understand that the domain of a function is a list of all the possible values you can put in (in other words, all the possible x values) and that the range is a list of all the possible values you can get out (in other words, all the possible y values)?
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  5. #5
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    Re: Function

    ive got this but im unsure if im correct or along the right track.

    y1 domain -3<x<3. range all positive real numbers<=3
    x=+-3 asymptotes

    y2 domain all real numbers not = 2
    range all real numbers
    x=2 asymptote
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  6. #6
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    Re: Function

    Quote Originally Posted by mikel03 View Post
    ive got this but im unsure if im correct or along the right track.

    y1 domain -3<x<3. range all positive real numbers<=3
    x=+-3 asymptotes

    y2 domain all real numbers not = 2
    range all real numbers
    x=2 asymptote
    y1 domain is correct. You are also correct that x = -3 and x = 3 are vertical asymptotes. The range is incorrect. Have you tried looking at a graph of the function?

    y2 domain is correct and x = 2 is an asymptote. The range is incorrect. I suggest you try long dividing to get the function into a form that is easier to analyse...
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  7. #7
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    Re: Function

    Thanks for your help but im unsure ive tried multiple times to solve the range and i got the same asnwer.

    can you please identify what im doing wrong
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  8. #8
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    Re: Function

    Quote Originally Posted by mikel03 View Post
    Thanks for your help but im unsure ive tried multiple times to solve the range and i got the same asnwer.

    can you please identify what im doing wrong
    \displaystyle \frac{1}{\sqrt{9 - x^2}} will be at its minimum where \displaystyle \sqrt{9 - x^2} is at its maximum. You should recognise this as the upper half of a circle, what is its maximum value?
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