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Math Help - Domain and Range Functions

  1. #1
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    Domain and Range Functions

    I am to write this in interval notation. I don't remember learning this:
    But here are two examples. On a graph, i know how to get the domain and range, but not from a function.

    f(x) = -4 -the radical(9-(x^2))

    g(x) = SIN the radical(x^2(-1)
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by sgonzalez90 View Post
    I am to write this in interval notation. I don't remember learning this:
    But here are two examples. On a graph, i know how to get the domain and range, but not from a function.

    f(x) = -4 -the radical(9-(x^2))

    g(x) = SIN the radical(x^2(-1)
    Recall that the domain of a function is all possibilities of x at which f(x) is defined:

    f(x)=-4-\sqrt{9-x^2}
    where is this function defined? Well, you know that you can't take the sqrt of a negative number, s f(x) is defined every where that 9-x^2\geq0\Rightarrow\mid{x}\mid\leq{3}. (If x where any bigger than 3, 9-x^2 would be less than zero. A big no no unless we're considering complex numbers.)

    In interval notation: [-3,3]

    you can do the other now can't you?
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  3. #3
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    Quote Originally Posted by VonNemo19 View Post
    Recall that the domain of a function is all possibilities of x at which f(x) is defined:

    f(x)=-4-\sqrt{9-x^2}
    where is this function defined? Well, you know that you can't take the sqrt of a negative number, s f(x) is defined every where that 9-x^2\geq0\Rightarrow\mid{x}\mid\leq{3}. (If x where any bigger than 3, 9-x^2 would be less than zero. A big no no unless we're considering complex numbers.)

    In interval notation: [-3,3]

    you can do the other now can't you?
    great, I understand the concept. But how do we solve for the range?
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Solve for x and then determine what y cannot be:

    y=-4-\sqrt{9-x^2}

    y+4=-\sqrt{9-x^2}

    (-y-4)^2=9-x^2

    (-y-4)^2-9=-x^2

    \pm\sqrt{-y^2-8y-7}=x

    \pm\sqrt{-[(y+7)(y+1)]}=x

    This one requires alittle more thought..........

    Ask yourself:

    When is the expression under the radical sign negative?
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  5. #5
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    For range I usually look at its graph, or plug values of x into my head.

    y=-4-\sqrt{9-x^2}

    The domain is [-3, 3]. If you look at \sqrt{9-x^2} only, what is its minimum value? It's 0, when x is -3 or 3. The maximum value? It's 3, when x = 0.

    Now consider the whole function. If you plug in x = -3 or 3, you actually get the maximum value of the function, because there is a negative in front of the square root:
    y=-4-\sqrt{9-9} = -4
    Plug in 0 for x to get the minimum value of the function:
    y=-4-\sqrt{9-0} = -7
    The range is [-7, -4].


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