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Math Help - Domain and Range

  1. #1
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    Domain and Range

    Can anyone explain domain and range to me. I know what it is and I can sort of tell from look at a graph what the domain is but i never get it 100% right. An example would be 5x+4/x^(1/2)+3x-2. Really anything you can tell me about domain and range and how to find it and put it in the correct intervals would be great.
    Thanks
    AC
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Casas4 View Post
    Can anyone explain domain and range to me. I know what it is and I can sort of tell from look at a graph what the domain is but i never get it 100% right. An example would be 5x+4/x^(1/2)+3x-2. Really anything you can tell me about domain and range and how to find it and put it in the correct intervals would be great.
    Thanks
    AC
    see the explanations of domain and range in the following threads:

    http://www.mathhelpforum.com/math-he...lus-notes.html (post #2)

    http://www.mathhelpforum.com/math-he...ain-range.html

    http://www.mathhelpforum.com/math-he...ions-help.html

    http://www.mathhelpforum.com/math-he...-function.html

    http://www.mathhelpforum.com/math-he...ain-range.html


    you should know how to find the domain and range for several classes of functions: polynomials, logs, radical, rationals, trigonometric functions. i think the threads i gave cover them all. if not, ask about them
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  3. #3
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    Quote Originally Posted by Casas4 View Post
    Can anyone explain domain and range to me. I know what it is and I can sort of tell from look at a graph what the domain is but i never get it 100% right. An example would be 5x+4/x^(1/2)+3x-2. Really anything you can tell me about domain and range and how to find it and put it in the correct intervals would be great.
    Thanks
    AC
    Domain is the values of "x" for which a function f(x) function has some defined answer. Range is the values of the function f(x) for a defined domain.
    Please note that for:
    y\;=\;5x + \frac{4}{\sqrt {x}} + 3x - 2
    For domain, the term inside the root should be positive
    x>0
    Also demoninator should not be equal to zero,
    x not = 0
    Therefore, Domain = {x belongs to real number R / x > 0}
    Range = {y belongs to real number R / x > 0}

    See another example:
    y\;=\;5x + \sqrt {3x - 2}
    Here, for domain, the term inside the root should be positive

    \;3x - 2 > 0

    \;x > \frac{2}{3}
    So, Domain = { {x\;belongs\;R/x > \frac{2}{3}}}

    Calculate y for \;x = \frac{2}{3}

    we got \;y = \frac{10}{3}

    So Range = { {y\;belongs\;R/y > \frac{10}{3}}}

    OK, See one more example
    y\;=\;(3x - 1)^{2}-5
    Here for domain, we can put any value of x, either positive, zero or negative, in the equation, we will get an answer for y.
    therefore Domain = {x belongs to real number R}
    For Range, We know that y\;=\;(3x - 1)^{2}>0 for any value of x. It is zero if \;x = \frac{1}{3}

    Therefore the minimum value of y will be 0 - 5
    i. e. y= -5

    So Range= { {y\;belongs\;R/y > -\;5}}
    Last edited by Shyam; August 26th 2008 at 08:42 PM.
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