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Math Help - Finding the range of a relation

  1. #1
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    Finding the range of a relation

    I have troubles in working out the range of the following relations:

    y=x-a, x<0, a>0

    y=(a/x)+a, a>0

    May you please list out the steps because I really want to understand the way~

    Also:

    y=square root x, x>_0 ---> Shouldn't the range be "all real numbers"? I saw the answer is [0,infinity[

    (Because for example, assuming that x=81, so y=square root 81, which equals either (-9) or (9), meaning that negative numbers are also accepted, so I think it is "all real numbers") Am I right?
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    Re: Finding the range of a relation

    Quote Originally Posted by kevinlam2490 View Post
    I have troubles in working out the range of the following relations:

    y=x-a, x<0, a>0

    y=(a/x)+a, a>0

    May you please list out the steps because I really want to understand the way~

    Also:

    y=square root x, x>_0 ---> Shouldn't the range be "all real numbers"? I saw the answer is [0,infinity[

    (Because for example, assuming that x=81, so y=square root 81, which equals either (-9) or (9), meaning that negative numbers are also accepted, so I think it is "all real numbers") Am I right?
    For the first, what would the range of \displaystyle y = x be if you restrict \displaystyle x < 0? Then translate this graph downward \displaystyle a units.

    For the second, think of the graph \displaystyle y = \frac{1}{x}. What is the range of this graph? A dilation will not change the range, but a translation of \displaystyle a units up will.

    For the third, the square root FUNCTION is defined as \displaystyle y = +\sqrt{x}. What is the range when only the top half of the parabola is used?
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