Math

posted by .

How can I find the asymptotes of [f(x) = 1/ (1+e^-x)]?

  • Math -

    f(x) = 1/(1 + e^-x)

    check for vertical asymptotes,
    to have those, the denominator has to be zero, so
    1+ e^-x = 0
    e^-x = -1
    or 1/e^x = 1/-1
    e^x = -1
    no solution , ---> if we take ln of both sides to solve for x, we would have to take ln(-1) which is undefined
    Therefore, no vertical asymptotes
    f(0) = 1/(1+1) = 1/2, so we have a y-intercept of 1/2

    let's look at far right and far left.
    as x ---> +∞
    e^-x ----> 0
    and 1/(1+e^-x) ----> 1

    as x ----> -∞
    e^-x ---> ∞
    and 1/(1+e^-x) --- 1/very large --> 0

    as x----> +∞ , f(x) --->1
    as x ----> -∞ , f(x) ---> 0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Cal(Please check)

    1) Find the Asymptotes: y = -2 sec 2pi x pi/2b and 3pi/2b pi/2(2pi) = pi/4 and 3pi/4 Is this correct?
  2. Math - asymptotes

    Identify all asymptotes. 1. y= 1 / 2-√x^2 - 3x the asymptotes I got were: vertical: 1 & 4 horizontal: 0 Is this it or are there more?
  3. trig

    I need to state the period and 2 consecutive asymptotes on the graph for the following questions. 1: y = -3 tan pi*x period: pi (?
  4. Math - Domain and Asymptotes

    Given the following rational function: f(x) = (x^2 + 6x - 8) / (x – 5) (a) state the domain. (b) find the vertical and horizontal asymptotes, if any. (c) find the oblique asymptotes, if any.
  5. TRIG

    I need to state the period and 2 consecutive asymptotes on the graph for the following questions. 1: y = -3 tan pi*x period: pi (?
  6. Math

    All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0. A. horizontal asymptotes B. polynomial C. vertical asymptotes D. slant asymptotes Is the answer D. vertical asymptotes?
  7. Geomatry

    For each of the rational functions find: a. domain b. holes c. vertical asymptotes d. horizontal asymptotes e. oblique asymptotes f. y-intercept g. x-intercepts 1. f(x)= x^2+x-2 / x^2-x-6
  8. algebra

    For each of the rational functions find: a. domain b. holes c. vertical asymptotes d. horizontal asymptotes e. oblique asymptotes f. y-intercept g. x-intercepts 1. f(x)= x^2+x-2 / x^2-x-6
  9. Math-asymptotes

    hi! so I have a rational equation : y = -3/x+1 and i'm wondering how you find the horizontal and vertical asymptotes.
  10. Math

    find a rational function that satisfies the given conditions vertical asymptotes x=-6,x=7 horizontal asymptotes y=10/9 x intercepts (6,0)

More Similar Questions