1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: How to find a function of f with the following characteristics

  1. Aug 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Give an expression for a function f which has all the following characteristics:

    f (0) = 4 , and
    f is increasing for x < 0 , and decreasing for x > 0 , and
    y = 1 is a horizontal asymptote of the graph of f as x→-∞ , and
    y = 0 is a horizontal asymptote of the graph of f as x→∞ .

    2. Relevant equations
    Any I guess

    3. The attempt at a solution

    Ok, since part a was to do with trigonometry I figured this being part b might follow suit but after having tried 4cos(x), 4/cos(x) and several other differing equations revolving around some manipulation of cos(0)=1 I've come up totally empty.

    So then I tried all manner of sorts of x+4 and 1/x +4 but still nothing.

    I'm not even sure of where to exactly start or how to approach this question aside from trial and error. I can find several equations to fit each characteristic but combining them is stumping me. The only other thing I can think of is a piece wise equation but again I'm not sure how to approach it or where to start.

    Tips and hints on where to begin are all I'm after, as long as I know I'm on the right path.
  2. jcsd
  3. Aug 28, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi dazza555! :smile:
    piecewise is fine :smile:

    (nothing in the question requires the answer to have a continuous derivative)

    and can you think of a function with f(0) = 0 and f(+∞) = 1 ? :wink:
  4. Aug 28, 2011 #3
    Thank you tiny-tim, that helps quite a bit. I shall work on it some more and post back early tomoz of how I go.
  5. Aug 30, 2011 #4
    Ok, so I've come up with the following piecewise equation:

    f(x)= 4 / e^(x^2), x>=0

    1 - 1/e^(x^2), x<0

    I'm fairly confident it satisfies all the criteria but I know I'll feel better once somebody confirms it (especially the "f(x) is increasing for x < 0 , and decreasing for x > 0" part).
  6. Aug 30, 2011 #5


    User Avatar
    Science Advisor
    Homework Helper

    hi dazza555! :smile:

    (try using the X2 icon just above the Reply box :wink:)
    (wouldn't it be better to write them as 4e-x2 and 1 - e-x2 ? :wink:

    and why not use x or -x instead of x2 ?)

    the first one is ok, but the second is decreasing, from 1 at -∞ to 0 at 0

    (and they aren't continuous at 0 … i know the question doesn't actually specify that, but it would be neater if it was continuous)
  7. Aug 30, 2011 #6
    I'm an idiot, I can't believe I missed that bit on the second piece, I've just assumed graph go up, graph increasing. Well it's a simple fix, if I change my second part to 1+3e-x2 it's all fixed and it'll be continuous at (0,0).

    The reason I chose x2 is because it gives a nice bell shape curve rather than a sharp spike up. Since I'm graphing it also on a rather small axis I figured this way I wont get marked down because it looks linear. Also the reason I wrote it as 4/e^(x^2) was because I failed to notice the superscript button and it kinda looked confusing with little hats going everywhere. But the constructive criticism is welcome, without it I never would've looked for it:wink:
  8. Aug 30, 2011 #7
    Also thanks for all the help tiny-tim.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook