Results 1 to 9 of 9
Like Tree8Thanks
  • 2 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By pumbaa213
  • 3 Post By johng

Math Help - How to solve this inequality question using a Graphic calculator?

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Unknown
    Posts
    73
    Thanks
    2

    Exclamation How to solve this inequality question using a Graphic calculator?

    e^(x+1) >/= (2-x)/(x-1)

    My textbook gives these instructions :

    Sketch the 2 equations on the same diagram and find x-coordinate of all intersections.
    Since e^(x+1) is greater or equals to (2-x)/(x-1),
    write the range of x such that e^(x+1) is higher than (2-x)/(x-1).


    I know how to whole thing goes and all but im not quite sure how to determine which range of numbers to draw out from the graph.
    Please help? thank you very much!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: How to solve this inequality question using a Graphic calculator?

    Your calculator should show you that the two functions intersect where:

    x\approx1.10829335987750907561302138

    Given the fact that the rational function has a vertical asymptote at x=1, and a horizontal asymptote at y=-1, on what interval(s) is the exponential function greater than or equal to the rational function?

    How to solve this inequality question using a Graphic calculator?-pumbaa213.jpg
    Last edited by MarkFL; July 11th 2013 at 06:50 PM.
    Thanks from pumbaa213 and topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2013
    From
    Unknown
    Posts
    73
    Thanks
    2

    Re: How to solve this inequality question using a Graphic calculator?

    Thanks for the help so far!
    Yes. this is exactly where im stuck!
    I do not know how to find the intervals.

    My teacher taught us the method of shading. But how do i know where to shade?
    Thank you very much! I hope im not confusing you.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: How to solve this inequality question using a Graphic calculator?

    You could shade along the x-axis for all those points in which the exponential function has a greater value than the rational function. Can you state what you think the intervals are?
    Thanks from pumbaa213
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2013
    From
    Unknown
    Posts
    73
    Thanks
    2

    Re: How to solve this inequality question using a Graphic calculator?

    Could it be x<1 or x>1.12?
    Thank you!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: How to solve this inequality question using a Graphic calculator?

    You have the right idea.

    x < 1 is correct, and I would, for the other interval, round to 1.11 instead and use a weak inequality (≥) since both functions are defined there and the original inequality is weak.

    Are you expected to give the solution in interval or set-builder notation?
    Thanks from pumbaa213
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Mar 2013
    From
    Unknown
    Posts
    73
    Thanks
    2

    Re: How to solve this inequality question using a Graphic calculator?

    In interval but yup i got it!
    Thanks thanks thanks so much for the help!
    Thanks from MarkFL
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    709
    Thanks
    294

    Re: How to solve this inequality question using a Graphic calculator?

    Hi,
    Here's another way to solve inequalities graphically; I think it's worthwhile adding to your arsenal. Transform the given inequality to one with 0 on one side. Let f(x) be the non-zero side. For example,

    e^{x+1}\geq{2-x\over x-1} becomes e^{x+1}-{2-x\over x-1}\geq0 and f(x)=e^{x+1}-{2-x\over x-1}

    Now list in increasing order all x's with f(x)=0 or f(x) undefined. This gives you a set of open intervals. Choose one point c in each interval and find the sign of f(c). Then f(x) has the same sign as f(c) for all x's in the open interval containing c.

    The above works for "nice" functions; if you go on and take calculus, you'll learn what I mean by "nice" functions. This is not a graphical solution, but it does provide a check on your reading of the graph of f(x). The attachment shows this method of attack:

    How to solve this inequality question using a Graphic calculator?-mhfalgebra1.png
    Thanks from MarkFL, pumbaa213 and topsquark
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Mar 2013
    From
    Unknown
    Posts
    73
    Thanks
    2

    Re: How to solve this inequality question using a Graphic calculator?

    Thanks johng! I found that helpful
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivatives, Slope/Tangent Graphic Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2013, 09:55 AM
  2. Replies: 2
    Last Post: October 4th 2012, 09:56 PM
  3. Replies: 2
    Last Post: May 6th 2012, 03:16 PM
  4. Replies: 3
    Last Post: February 28th 2011, 10:02 AM
  5. Solve cos x = x with a calculator
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: April 16th 2008, 08:53 AM

Search Tags


/mathhelpforum @mathhelpforum