Pre-Cal


use a graphing calculator to obtain the graph of the function. What do you observe about its asymptotes?

g(x) = 4 [x-2] / x + 1

My answer was there are two horizontal asymptotes. My teacher said that there are two asymptotes but she wants me to find the equation for them. I do not understand what she means.

asked by Hannah
  1. If x is alone at the bottom, you have vertical asymptotes at x = 0
    if (x+1) is on the bottom, they are at x = -1
    There are no horizontal asymptotes here.

    posted by Damon
  2. x = 0 is the equation of a vertical asymptote for example, graph it.

    posted by Damon
  3. I have to disagree with Damon, although he is usually right.

    If your equation is
    y = 4(x-2)/(x+1) there is a horizontal asymptote of
    y = 4

    If you equation is
    y = 4(x-2)/x + 1 as you typed it,
    there is a horizontal asymptote of
    y = 5

    posted by Reiny
  4. Sorry. I only really looked at the x singularity.
    Of course if x gets big positive or negative y approaches 4 (x/x) if you have (x-2)/(x+1)

    posted by Damon

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