Results 1 to 2 of 2

Math Help - Range and Domain

  1. #1
    Newbie
    Joined
    Mar 2009
    From
    bangalore, India
    Posts
    3

    Range and Domain

    1. Graph the parabola y=x-x^2. Then find the domain and range of f(x)=sqrt(x-x^2).

    2. Graph the parabola y=3-2x-x^2. Then find the domain and range of g(x)=sqrt(3-2x-x^2).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    y=x-x^2=x(1-x)

    This means the parabola equals 0 at x=1 and x=0 (this should help graph it). A graph shows that between x=1 and x=0 y is positive.

    \frac{d}{dx} x-x^2=1-2x

    Stationary point: 1-2x=0 \Rightarrow \ x=\frac{1}{2}.

    The stationary point (it's a maximum, you can prove that part) is \left( \frac{1}{2}, \frac{1}{4} \right). This is the second part of the graph and comes in handy later!

    The transformation is f(x)=\sqrt{x-x^2} but we know that y=x-x^2. Hence the transformation is f(y) = \sqrt{y}.

    The domain therefore is \{ x \in \mathbb{R}: \ 0 \leq x \leq 1 \} (otherwise we would have the square root of something negative).

    The range is \{ f(x) \in \mathbb{R}: \ f(x) \leq \frac{1}{2} \}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Domain and range
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 14th 2010, 03:09 AM
  2. Domain and Range
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: January 13th 2010, 08:12 AM
  3. Replies: 6
    Last Post: September 16th 2009, 07:25 AM
  4. Domain And Range
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: May 3rd 2008, 10:31 PM
  5. Domain and range?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 22nd 2008, 05:45 AM

Search Tags


/mathhelpforum @mathhelpforum