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Thread: Help w Functions: math progr. says -x+y^2=2 is function

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    Help w Functions: math progr. says -x+y^2=2 is function

    I was doing this math program, and I got problems about whether a certain equation was a function. -x+y^2=2 was considered a function, and y=sqrt(x+1) was also considered a function. I don't get how. When solving square roots, don't we have to consider the positive or negative solution? Thanks in advance.

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    -x+y^2=2 is not a function but it is a conic which is a union of two functions
    conic= parabola
    hyperbola
    ellipse
    circle
    the equation+y^2=2 is a parabola(graph below)
    ScreenCapture_2017-08-22_17.47.05.jpg
    -x+y^2=2 can be written as y=squr(x+2) and y=-squr(x+2)
    for y=squr(x+2) the graph is like that ScreenCapture_2017-08-22_17.48.05.jpg

    for y=-squr(x+2) the graph is like that ScreenCapture_2017-08-22_17.50.19.jpg

    therefore as you notice that these 2 graphs are the union of the 1st
    these graphs are called functions while the 1st one is a conic
    a function is not a function when a vertical line cuts it at 2 points

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    Quote Originally Posted by jennie View Post
    I was doing this math program, and I got problems about whether a certain equation was a function. -x+y^2=2 was considered a function, and y=sqrt(x+1) was also considered a function. I don't get how. When solving square roots, don't we have to consider the positive or negative solution? Thanks in advance.
    the equation -x+y^2=2 is not a function
    it is a conic(parabola,hyperbola,ellipse,circle)
    -x+y^2=2 can be written as y=squ(x+2) and y=-squ(x+2)
    -x+y^2=2 is the union of y=squ(x+2) and y=-squ(x+2)
    example by graph:
    > -x+y^2=2 ScreenCapture_2017-08-22_17.47.05.jpg

    > y=squ(x+2) ScreenCapture_2017-08-22_17.48.05.jpg



    > y=-squ(x+2) ScreenCapture_2017-08-22_17.50.19.jpg



    as you see that the 1st graph is the union of the 2nd and the 3rd one
    remark:the 2nd and the 3rd equations are function but the first is not
    an equation is not a function when a vertical line cuts its graph at two points

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    Quote Originally Posted by jennie View Post
    I was doing this math program, and I got problems about whether a certain equation was a function. -x+y^2=2 was considered a function, and y=sqrt(x+1) was also considered a function. I don't get how. When solving square roots, don't we have to consider the positive or negative solution? Thanks in advance.
    The square root function is always considered to be non-negative.

    [tex](-\ 2)^2 = 4 \implies (-\ 2) = -\ \sqrt{4} \ne \sqrt{4} = 2.[/tex]

    in other words

    [tex]x^2 - 4 = 0[/tex] has two roots, the square root and its additive inverse.

    EDIT: Your first example can be shown as a valid function only as f(y) = x. Do you see why?
    Last edited by JeffM; 08-23-2017 at 12:19 AM.

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    Quote Originally Posted by jennie View Post
    When solving square roots, don't we have to consider the positive or negative solution?
    Yes, if you solve y^2 = 2 - x for y, by taking the square root of each side, then you do need to consider both the square root of 2-x and its opposite. This generates two functions, as explained below.

    In the relationship between x and y given by the equation

    x + y^2 = 2

    it's true that y is not a function of x. Rather, as JeffM posted, x is a function of y.

    However, if we restrict the values of y to be non-negative, then y is a function of x.

    Alternatively, if we restrict y to be negative, then y becomes a different function of x.

    y1(x) = sqrt(2 - x)

    y2(x) = - sqrt(2 - x)

    The domain for each of these functions is all numbers less than or equal to 2.

    The range for y1(x) is all non-negative numbers.

    The range for y2(x) is all negative numbers and zero.

    Sent from my SM-G920V using Tapatalk

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    Cool

    Quote Originally Posted by jennie View Post
    I was doing this math program, and I got problems about whether a certain equation was a function. -x+y^2=2 was considered a function...
    We can only speak to the general definition of functions, using the common orientation of variables. We can't speak to whatever math program you're using, nor how it defines the variables; especially since we don't know what you've entered, how the program is set up, or what is meant by "is considered a function".

    If you could provide all of the necessary information, we may be able to assist. But, with the current information, I can only suggest that perhaps the software is fluid with the variables (because "-x + y^2 = 2" is a function, of x in terms of y).

    Quote Originally Posted by jennie View Post
    and y=sqrt(x+1) was also considered a function. I don't get how. When solving square roots, don't we have to consider the positive or negative solution?
    Are you saying that you'd started out with "y^2 = x + 1", and then took one of the square roots? Because, if you'd started with "y = sqrt[x + 1]", then there is nothing to "solve"; you've already been given a function (of y in terms of x).

    Please reply with clarification. Thank you!

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