Results 1 to 2 of 2

Math Help - How to find the range of a function?

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    How to find the range of a function?

    Hello i got no problem with domain and im a bit of confused on how to find the range of a function given:
    f(x) = \sqrt{4-x^2}
    the answer is [0,2]

    cud u please explain how its done? i really dont understand how to find the range

    Ive got another question:
    Why is x = y^2 not a function and x = y^3 is?
    Last edited by ^_^Engineer_Adam^_^; November 9th 2006 at 03:41 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Hello i got no problem with domain and im a bit of confused on how to find the range of a function given:
    f(x) = \sqrt{4-x^2}
    the answer is [0,2]

    cud u please explain how its done?
    Here is a simple explaination.
    y=\sqrt{4-x^2}
    When you square it you have,
    y^2=4-x^2
    x^2+y^2=2^2
    A circle!
    Of radius 2.

    But the original function,
    y=\sqrt{4-x^2}
    Is a semi-circle because we only take the positive side of the circle (since square root only returns positive values).

    Since the radius it 2 it starts at zero and goes all the way until 2.

    Why is x = y^2 not a function and x = y^3 is?
    The curve x=y^2 cannot be a function. Because for example, (-4,2),(-4,-2) lie on this curve. Thus, for an absicca (x) values we have two ordinate (y) values which means it cannot be a function.

    The other curve only has one value.
    Because when you have x=y^3 the only solution (real) for y is y=\sqrt[3]{x}.

    While in the first curve there are two solutions for y, y=\pm \sqrt{x} (because it has even degree).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the domain and range of the function
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 8th 2011, 05:38 AM
  2. Replies: 7
    Last Post: March 27th 2010, 01:52 PM
  3. Replies: 1
    Last Post: November 15th 2009, 12:49 PM
  4. Replies: 1
    Last Post: September 25th 2009, 03:46 AM
  5. Find the range of a function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 7th 2006, 06:23 PM

Search Tags


/mathhelpforum @mathhelpforum