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Thread: Domain And Range

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    Domain And Range

    hello, i need some help with this problem please!!:

    Given

    y= 1/x-3

    a)find the domain
    b)find the range


    thanks
    Last edited by subzero06; May 3rd 2008 at 07:58 PM.
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    Quote Originally Posted by subzero06 View Post
    y= 1/x-3
    Do you mean $\displaystyle y = \frac{1}{x} - 3$ (as it's written) or $\displaystyle y = \frac{1}{x - 3}$?

    In either case, the domain is the set of values of $\displaystyle x$ for which the function is defined. Notice that you have a variable in the denominator of your function. Since division by zero is undefined, what does that tell you about the values that $\displaystyle x$ can take on?

    The range will be all of the possible values of $\displaystyle y$. For $\displaystyle y = \frac{1}{x} - 3$, note that $\displaystyle \frac{1}{x}$ can never be zero; what does that tell you about the possible values of $\displaystyle y$?
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    Quote Originally Posted by Reckoner View Post
    Do you mean $\displaystyle y = \frac{1}{x} - 3$ (as it's written) or $\displaystyle y = \frac{1}{x - 3}$?

    In either case, the domain is the set of values of $\displaystyle x$ for which the function is defined. Notice that you have a variable in the denominator of your function. Since division by zero is undefined, what does that tell you about the values that $\displaystyle x$ can take on?

    The range will be all of the possible values of $\displaystyle y$. For $\displaystyle y = \frac{1}{x} - 3$, note that $\displaystyle \frac{1}{x}$ can never be zero; what does that tell you about the possible values of $\displaystyle y$?
    yeah the second 1
    y=1/(x-3)

    so X cannot be 3? so is any number not = 3?
    and Y is any number but not zero?
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    Quote Originally Posted by subzero06 View Post
    yeah the second 1
    y=1/(x-3)

    so X cannot be 3? so is any number not = 3?
    and Y is any number but not zero?
    Yes.
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    Quote Originally Posted by subzero06 View Post
    yeah the second 1
    y=1/(x-3)

    so X cannot be 3? so is any number not = 3?
    and Y is any number but not zero?
    Correct! The domain is all real numbers $\displaystyle x\neq3$, and the range is all real numbers $\displaystyle y\neq0$. Good job.
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