1. 19th hole
    Joined
    07 Mar '07
    Moves
    32955
    03 Oct '08 02:341 edit
    Actually this isn't a riddle, but a question I have concerning the graphing of an equation. If you graph a function in the y=1/x function family, something like y=(2x-7)/(3x+4), how do you determine the horizontal asymptote of the graph? The vertical asmphtote is easy enough (x=-4/3), but I am not sure how to get the horizontal one. I hope that this question makes sense...
  2. Joined
    01 May '07
    Moves
    27311
    03 Oct '08 02:411 edit
    Originally posted by UserChevy
    Actually this isn't a riddle, but a question I have concerning the graphing of an equation. If you graph a function in the 1/x function family, something like (2x-7)/(3x+4), how do you determine the horizontal asymptote of the graph? The vertical asmphtote is easy enough (x=-4/3), but I am not sure how to get the horizontal one. I hope that this question makes sense...
    If I remember correctly it would be the variable in the numerator divided by the variable in the denominator, if that makes sense. It has been three years, however, so I may be wrong. In your case:

    Original Equation =

    (2x-7)
    -------
    (3x+4)

    Horizontal Asymptote =

    2x
    ---
    3x

    so

    2
    --
    3
  3. Joined
    15 Feb '07
    Moves
    667
    03 Oct '08 03:12
    (2x-7)/(3x+4)
    (6x-21)/(9x+12)
    (6x+8-29)/(9x+12)
    (6x+8)/(9x+12) - 29/(9x+12)
    2/3 - 29/(9x+12)

    The horizontal asymptote would be y=2/3.
  4. 19th hole
    Joined
    07 Mar '07
    Moves
    32955
    03 Oct '08 10:29
    That makes sense, thanks for both answers.
  5. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
    Moves
    7733
    03 Oct '08 14:101 edit
    Originally posted by UserChevy
    That makes sense, thanks for both answers.
    yeah..in general

    if you have n(x)/d(x) = ax^m/bx^n

    if m > n, then H.A does not exist

    if m=n , then H.A. = a/b

    if m< n, then HA is line y=0

    if m > n there is a slant asymptote.. to obtain it, use long division for algebraic expressions

    you will get an equation of a line + some remainder and then take the limit as x approaches + or - infinity and you get the slant (oblique asymptote)

    don't know if you wanted all that, but it cant hurt!!
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