Results 1 to 6 of 6

Thread: z As Function of x and y

  1. #1
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    317
    Thanks
    4

    z As Function of x and y

    Determine if z is a function of x and y.

    1. x^2 z + yz - xy = 10

    I say no because there are two z letters in the equation.

    2. (x^2/4) + (y^2/9) = 1

    I say yes for number 2 but do not know why.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,587
    Thanks
    2596

    Re: z As Function of x and y

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

    1. x^2 z + yz - xy = 10

    I say no because there are two z letters in the equation.
    Therefore what?
    What does that have to do with determining whether or not z is a function of x and y?
    (x^2+ y)z= xy+ 10
    z= (xy+ 10)/(x^2+ y).

    Now, what does that have to do with determining whether or not z is a function of x and y?

    2. (x^2/4) + (y^2/9) = 1

    I say yes for number 2 but do not know why.
    Given values for x and y, how would you calculate a value of z? Did you notice that there is NO z in that formula?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    317
    Thanks
    4

    Re: z As Function of x and y

    Quote Originally Posted by HallsofIvy View Post
    Therefore what?
    What does that have to do with determining whether or not z is a function of x and y?
    (x^2+ y)z= xy+ 10
    z= (xy+ 10)/(x^2+ y).

    Now, what does that have to do with determining whether or not z is a function of x and y?


    Given values for x and y, how would you calculate a value of z? Did you notice that there is NO z in that formula?
    Question 2 should be (x^2/4) + (y^2/9) + z^2 = 1
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    317
    Thanks
    4

    Re: z As Function of x and y

    Quote Originally Posted by HallsofIvy View Post
    Therefore what?
    What does that have to do with determining whether or not z is a function of x and y?
    (x^2+ y)z= xy+ 10
    z= (xy+ 10)/(x^2+ y).

    Now, what does that have to do with determining whether or not z is a function of x and y?


    Given values for x and y, how would you calculate a value of z? Did you notice that there is NO z in that formula?
    We need to solve for z in each case and determine if it is a function of x and y. I will post my reply when time allows.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    317
    Thanks
    4

    Re: z As Function of x and y

    Question 1

    I think of a function as something that gives me a unique output value for a given input value. So, in this case, I can think of a function as something that gives me at most one unique value for z in terms of x and y.

    I can factor out z and rearrange terms as follows:

    z(x^2 + y) - xy = 4
    z(x^2 + y) = 4 + xy
    z = (4 + xy) / (x^2 + y)

    Since I am able to solve for the expression involving x and y that gives me one unique z, I say z is a function of x and y.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    May 2016
    From
    NYC
    Posts
    317
    Thanks
    4

    Re: z As Function of x and y

    Question 2




    My goal is to isolate z.

    z^2 = 1 - (x^2)/4 + (y^2)/9

    I must take the square root on both sides to yield z.

    z = sqrt(1 - (x^2)/4 + (y^2)/9)

    z = -sqrt(1 - (x^2)/4 + (y^2)/9)

    I needed to take the square root on both sides giving TWO answers for z as shown above. I conclude that in this case we do not always get a unique value for z.
    So, I say z is not a function of x and y.
    Last edited by USNAVY; Jan 13th 2017 at 08:08 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Apr 26th 2016, 09:16 PM
  2. Replies: 20
    Last Post: Nov 27th 2012, 06:28 AM
  3. Replies: 0
    Last Post: Oct 19th 2011, 05:49 AM
  4. Replies: 4
    Last Post: Oct 27th 2010, 06:41 AM
  5. Replies: 3
    Last Post: Sep 14th 2010, 03:46 PM

/mathhelpforum @mathhelpforum