Results 1 to 3 of 3

Math Help - Finding Domain and Range

  1. #1
    Newbie
    Joined
    Aug 2010
    From
    iligan.philippines
    Posts
    10

    Finding Domain and Range

    Please help me in finding the range of this equation.
    5y(x-109x-3) = 2(5x+3)
    I already got the domain which is x≠ 1,3.

    My problem is on how to get the range. This is what I started.
    5y(x-109x-3) = 2(5x+3)
    5y(x^2-4x+3) = 10x+15
    I stuck until here. I don't know if I did the right move.
    A friend told me that the range is y≤-5 but he could not show me the whole solution.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member pflo's Avatar
    Joined
    Apr 2009
    From
    Albuquerque, NM
    Posts
    155
    Thanks
    7
    Quote Originally Posted by vldo View Post
    Please help me in finding the range of this equation.
    5y(x-109x-3) = 2(5x+3)
    I already got the domain which is x≠ 1,3.

    My problem is on how to get the range. This is what I started.
    5y(x-109x-3) = 2(5x+3)
    5y(x^2-4x+3) = 10x+15
    I stuck until here. I don't know if I did the right move.
    A friend told me that the range is y≤-5 but he could not show me the whole solution.
    First off, I assume you are talking about the last equation you've written and not the first two. The domain would be wrong if you were talking about the first two.

    In calculus, you can find the domain by analyzing the derivatives of your function.

    First, find \frac{dy}{dx} and set it equal to zero to find all local maxima and minima. A first derivative test will tell you the function is decreasing from x=negative infinity to x=-3 (where it hits a minimum at (-3,-0.2)), then increasing untiil x=1 (there is a discontinuity at x=1), then increases until x=1.8 (where there is a maximum at (1.8,-5)), then decreases until x=3 (there is a disconuity at x=3), then decreases over the remainder of its domain.

    Can you picture this in your mind? Or even draw a quick sketch of this behavior?

    The only real question is whether the functional values pass between -0.2 and -5 when it is decreasing as x gets larger. Looking at the original function there is a horizontal asymptote at y=0, so it can't pass through these values.

    You can go through the same analysis of the second derivative to determine the intervals where the function is concave up and down. But the first derivative test will really tell you what you need to know for this function.

    The range is -0.2<=y<=-5.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    domain & range

    Quote Originally Posted by vldo View Post
    Please help me in finding the range of this equation.
    5y(x-109x-3) = 2(5x+3)
    I already got the domain which is x≠ 1,3.

    My problem is on how to get the range. This is what I started.
    5y(x-109x-3) = 2(5x+3)
    5y(x^2-4x+3) = 10x+15
    I stuck until here. I don't know if I did the right move.
    A friend told me that the range is y≤-5 but he could not show me the whole solution.

    After looking at my keyboard - to see what likely typos you made - I assume you typed 0 for ) and 9 for (. So you must mean:
    What is the range of 5y(x-1)(x-3) = 2(5x+3) ?

    Now solve for y - no need to expand (x-1)(x-3).

    \displaystyle y=\left({2\over 5}\right){{5x+3}\over{(x-1)(x-3)}}

    You have the domain right.

    There is a horizontal asymptote: y=0. However, this doesn't mean y\ne0. It only gives the behavior of y when |x|\to +\infty. In fact y=0 when x = -{3\over5}.

    As mentioned elsewhere, there is a local minimum at (-3,-0.2), and a local maximum at (1.8, -5). y does not take on any values between -5 and -0.2 .

    Therefore, y<=-5 OR y>=-0.2. In interval notation this is:

    Range = (-\infty,\ -5] \cup [-0.2,+\infty)
    .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding domain and range
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: July 11th 2010, 04:20 AM
  2. Finding Domain & Range
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 14th 2010, 11:03 PM
  3. Finding Domain and Range
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 4th 2009, 04:30 PM
  4. finding domain and range
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 8th 2008, 07:56 PM
  5. finding the domain and range
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 25th 2007, 06:35 PM

Search Tags


/mathhelpforum @mathhelpforum