Results 1 to 14 of 14
Like Tree6Thanks
  • 1 Post By topsquark
  • 1 Post By chiro
  • 1 Post By Prove It
  • 1 Post By chiro
  • 1 Post By chiro
  • 1 Post By HallsofIvy

Thread: z As Function of Two Variables

  1. #1
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    353
    Thanks
    5

    z As Function of Two Variables

    Determine if z is a function of x and y.

    1. xz^2 + 2xy - y^2 = 4

    I say yes because there is only one z letter in the equation.

    2. z + x lny - 8 = 0

    I have no idea about number 2.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,676
    Thanks
    2640

    Re: z As Function of Two Variables

    Quote Originally Posted by USNAVY View Post
    Determine if z is a function of x and y.

    1. xz^2 + 2xy - y^2 = 4

    I say yes because there is only one z letter in the equation.
    So what? What is your definition of "function"?

    2. z + x lny - 8 = 0

    I have no idea about number 2.
    z= 8- x ln(y)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    353
    Thanks
    5

    Re: z As Function of Two Variables

    Quote Originally Posted by HallsofIvy View Post
    So what? What is your definition of "function"?


    z= 8- x ln(y)
    I will get back to you on this post when time allows.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,970
    Thanks
    665
    Awards
    1

    Re: z As Function of Two Variables

    Quote Originally Posted by USNAVY View Post
    Determine if z is a function of x and y.

    1. xz^2 + 2xy - y^2 = 4

    I say yes because there is only one z letter in the equation.
    Echoing HallsofIvy's response, how are you defining a function? In the equation, for example, z^2 = y there is "only one z in the equation" but my example is not a function.

    -Dan
    Thanks from USNAVY
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    353
    Thanks
    5

    Re: z As Function of Two Variables

    Quote Originally Posted by topsquark View Post
    Echoing HallsofIvy's response, how are you defining a function? In the equation, for example, z^2 = y there is "only one z in the equation" but my example is not a function.

    -Dan
    I will reply in full tomorrow.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,415
    Thanks
    1676

    Re: z As Function of Two Variables

    Do you know the vertical line test for a function?
    Thanks from USNAVY
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,787
    Thanks
    1914

    Re: z As Function of Two Variables

    Quote Originally Posted by chiro View Post
    Do you know the vertical line test for a function?
    For a 3D problem like this, you would have to think about using a horizontal plane test...
    Thanks from USNAVY
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    353
    Thanks
    5

    Re: z As Function of Two Variables

    Quote Originally Posted by chiro View Post
    Do you know the vertical line test for a function?
    Yes, of course.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,415
    Thanks
    1676

    Re: z As Function of Two Variables

    That is correct for higher dimensions.

    Also - the implicit derivatives should be separable if you can have a function.
    Thanks from USNAVY
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    353
    Thanks
    5

    Re: z As Function of Two Variables

    Quote Originally Posted by HallsofIvy View Post
    So what? What is your definition of "function"?


    z= 8- x ln(y)
    A function relates an input to an output.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,415
    Thanks
    1676

    Re: z As Function of Two Variables

    You still have a vertical line test for a function but you will do it in the z-axis not the x or y.
    Thanks from USNAVY
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,676
    Thanks
    2640

    Re: z As Function of Two Variables

    Quote Originally Posted by USNAVY View Post
    A function relates an input to an output.
    A function relates an input to a unique output.
    Thanks from USNAVY
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    353
    Thanks
    5

    Re: z As Function of Two Variables

    I will post my answer to question 1 later.
    Last edited by USNAVY; Jan 13th 2017 at 08:03 AM.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    353
    Thanks
    5

    Re: z As Function of Two Variables

    I will post my answer to question 2 later.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A max function of 2 variables max(a,b)
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: Sep 27th 2011, 06:05 PM
  2. How to Solve for Function of Two Variables
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 14th 2011, 10:04 PM
  3. Replies: 3
    Last Post: Feb 18th 2011, 03:27 AM
  4. Maximizing a function of two variables
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Oct 5th 2009, 02:15 PM
  5. Function of two variables
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 17th 2009, 04:35 PM

/mathhelpforum @mathhelpforum