Results 1 to 2 of 2

Math Help - How do I graph a multivariable function?

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    13

    How do I graph a multivariable function?

    Sketch the graph and describe the vertical and horizontal traces.
    f(x,y) = y^2

    Is this simply a parabola that touches ONLY the yz-plane in R^3?
    Would the traces basically be:
    Horizontal:
    \pm\sqrt{c} = y } when z = c

    Vertical:
    z = y^2 \} when x = a
    z = b^2 \} when y = b
    Last edited by ZeroVector; October 24th 2010 at 04:21 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by ZeroVector View Post
    Sketch the graph and describe the vertical and horizontal traces.
    f(x,y) = y^2

    Is this simply a parabola that touches ONLY the yz-plane in R^3?


    It can't be a parabola since it is a 2-variables function and thus is a surface in \mathbb{R}^3. Take, for example, the

    values f(0,y). Here, you get the usual parabola on the yz plane...but it is THE SAME for ANY value of x, so you actually get

    a paraboloid every perpendicular to the xy-plane cut of which looks at the well-known parabola x=y^2.

    Go to the site Functions of Two Variables to see how this function looks.

    Tonio



    Would the traces basically be:
    Horizontal:
    \pm\sqrt{c} = y } when z = c

    Vertical:
    z = y^2 \} when x = a
    z = b^2 \} when y = b
    .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multivariable Calc Image-Graph Problem.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 14th 2010, 10:15 AM
  2. Graph of a Multivariable Equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 11th 2010, 06:36 PM
  3. Multivariable function fun;
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: October 5th 2009, 09:56 AM
  4. sketching a multivariable graph
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2008, 08:30 AM
  5. Maximum value of a multivariable function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 2nd 2008, 07:47 PM

/mathhelpforum @mathhelpforum