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Math Help - cubed root domain and range

  1. #1
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    cubed root domain and range

    i have a cubed root funtion i cannot figure out if the domain and range are correct for.

    y=(√x)(x≤0)
    y=(-√x)(x√0)

    i tried the domain and got this.
    (-∞,0]
    (-∞,0]

    please help me find my range and let me know if my domain is correct, thank you
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  2. #2
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    Quote Originally Posted by paa13 View Post
    i have a cubed root funtion i cannot figure out if the domain and range are correct for.

    y=(√x)(x≤0)
    y=(-√x)(x√0)

    i tried the domain and got this.
    (-∞,0]
    (-∞,0]

    please help me find my range and let me know if my domain is correct, thank you
    Is this a hybrid function or two separate functions?
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    sorry, two seperate functions
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    Quote Originally Posted by paa13 View Post
    i have a cubed root funtion i cannot figure out if the domain and range are correct for.

    y=(√x)(x≤0)
    y=(-√x)(x√0)

    i tried the domain and got this.
    (-∞,0]
    (-∞,0]

    please help me find my range and let me know if my domain is correct, thank you
    I assume the second should have a \leq where the square root symbol is...

    You're told what the domains are. The domain is the set of values x can take. So in both cases, the domain is x\leq0. What you've written in interval notation is also fine.

    Remember that the cubed root of a number has the same sign as the original number itself. So the cube root of any negative number stays negative. That means that the range of the first is the same as the domain, i.e. y \leq 0.

    The second function is a reflection in the x-axis of the first.

    So the range of the second function is y \geq 0.
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    Quote Originally Posted by Prove It View Post
    I assume the second should have a \leq where the square root symbol is...

    You're told what the domains are. The domain is the set of values x can take. So in both cases, the domain is x\leq0. What you've written in interval notation is also fine.

    Remember that the cubed root of a number has the same sign as the original number itself. So the cube root of any negative number stays negative. That means that the range of the first is the same as the domain, i.e. y \leq 0.

    The second function is a reflection in the x-axis of the first.

    So the range of the second function is y \geq 0.
    how is that in interval notation, 1.(- infin.,0] and then 2.[0, infin.)
    do i have them in the wrong order?
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    Quote Originally Posted by paa13 View Post
    how is that in interval notation, 1.(- infin.,0] and then 2.[0, infin.)
    do i have them in the wrong order?
    (-\infty, 0] and [0, \infty) is correct.
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  7. #7
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    ty soo much, yer a life saver
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