Why does a radical function with an even index only appear on one side of the x-axis while a radical function with an odd index appears on ?

Why does a radical function with an even index only appear on one side of the x-axis while a radical function with an odd index appears on both sides?

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  • mizoo
    Lv 7
    4 weeks ago

    The radical with the even index has a restriction in the domain :  The expression inside the radical must be greater than or equal to zero.

    The radical with odd index doesn't have this restriction => the graph appears on both sides.

  • 4 weeks ago

    f(x) = √x

    Using that as an example, if x is negative we don't get a real value for f(x) since we can't get the square root of a negative number.

    So f(x) has no real values when x < 0, so that's why the graph only exists when x >= 0.

    When you have cube root,

    f(x) = ³√x

    the cube root of a negative number results in a negative real value, so this can be graphed for all values of x.

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