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Math Help - Understanding (Square root of X) on Graph

  1. #1
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    Understanding (Square root of X) on Graph

    I understand how these look on the graph.
    (The /, U, C are just an example of what they look like on the graph)
    Y = X looks like /
    Y = X^2 looks like U
    X = Y looks like /
    X = Y^2 looks like C

    However I don't understand why the (square root of X) looks the way it does on the graph.


    I also know that Negative (Square root of X) is flipped on the Y axis.

    Even though I know this, I don't understand why it ends up like this.

    Can anyone explain to me.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Brazuca View Post
    I understand how these look on the graph.
    (The /, U, C are just an example of what they look like on the graph)
    Y = X looks like /
    Y = X^2 looks like U
    X = Y looks like /
    X = Y^2 looks like C

    However I don't understand why the (square root of X) looks the way it does on the graph.


    I also know that Negative (Square root of X) is flipped on the Y axis.

    Even though I know this, I don't understand why it ends up like this.

    Can anyone explain to me.

    Yes you do. it looks like x=y^2 because x=y^2\Rightarrow{y}=\sqrt{x} (assuming y is positive). basic algebra.

    Remember that you can't take the square root of a negative number, so that's why you don't get the bottom half of the "C".
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  3. #3
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    Oh that makes sense.
    Last edited by Brazuca; July 21st 2009 at 07:04 PM.
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  4. #4
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    Quote Originally Posted by VonNemo19 View Post
    Yes you do. it looks like x=y^2 because x=y^2\Rightarrow{y}=\sqrt{x} (assuming y is positive). basic algebra.

    Remember that you can't take the square root of a negative number, so that's why you don't get the bottom half of the "C".
    Actually, that's not true. When you take the square root of a number, you actually get two answers, a positive one and a negative one.
    \text{Ex:}\;\;\sqrt{16}\;=\;{\color{red}\pm} 4

    But if we have two y-values for every single x-value, then we wouldn't have a function at all. The vertical line test would fail. So, to make the square-root a function, we take the positive answers only ( \sqrt{16}\;=\;{\color{red}+}4).

    While you are correct to say that you can't take a square root of a negative number, if we pretend for a moment that you can, then on the graph there would be a curve on the left side of the y-axis. I think that was what you meant to say.


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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yeongil View Post
    Actually, that's not true.
    Everything I said is true, and your post said it a different way.

    Note where I said (assuming y is positive).

    \sqrt{16}= \pm 4 <---------This is not true.


    Quote Originally Posted by yeongil View Post
    there would be a curve on the left side of the y-axis.
    Do you mean a reflection BELOW the X-axis?
    Last edited by VonNemo19; July 22nd 2009 at 07:05 PM.
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  6. #6
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    Quote Originally Posted by VonNemo19 View Post
    Note where I said (assuming y is positive).
    Oops, didn't see that before.

    there would be a curve on the left side of the y-axis.
    Do you mean a reflection BELOW the X-axis?
    I'm not explaining very well. You said this:
    Remember that you can't take the square root of a negative number, so that's why you don't get the bottom half of the "C".
    Not taking "the square of a negative number" means that x cannot take on negative values. Not getting "the bottom half of the "C"," to me, implies that the graph has no negative y values. This is my point of contention.

    The reason that the graph doesn't have a "bottom half of the "C"" is because we assume only positive values for y, as you pointed out earlier. To say that a function does not take on negative x-values means that there would be nothing to graph on the left side of the y-axis, because that's where the x-values are negative.

    Let's say, for example, that we have a function defined as:
    y = x^2,\;\;x \ge 0.
    Then saying this would be correct:
    Remember that by the definition above we are not permitted to square a negative number, so that's why you don't get the left half of the "U".

    Hopefully that made more sense. Apologies for the confusion.


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  7. #7
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yeongil View Post
    Oops, didn't see that before.



    I'm not explaining very well. You said this:

    Not taking "the square of a negative number" means that x cannot take on negative values. Not getting "the bottom half of the "C"," to me, implies that the graph has no negative y values. This is my point of contention.

    The reason that the graph doesn't have a "bottom half of the "C"" is because we assume only positive values for y, as you pointed out earlier. To say that a function does not take on negative x-values means that there would be nothing to graph on the left side of the y-axis, because that's where the x-values are negative.

    Let's say, for example, that we have a function defined as:
    y = x^2,\;\;x \ge 0.
    Then saying this would be correct:
    Remember that by the definition above we are not permitted to square a negative number, so that's why you don't get the left half of the "U".

    Hopefully that made more sense. Apologies for the confusion.


    01
    I agree with everything you say, but the op asked about a "C". I could have stated that \pm\sqrt{x}=y is not a function, but a relation, and therefore we must confine ourselves to the first quadrant. I merely told the op what he needed to hear so that he would better understand why there is no lower half of the "c".

    Again, what you say is true, but what I said is ALSO true.
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