+130511 Here's a closer look at a "split" graph of this......I have chosen to let "k" = 1, but it's value really doesn't have any effect on the end behavior.....
Note that because of the one denominator of "x" and the other of (x+1) that this graph will have vertical asymptotes at x =0 and x = -1 (as expected). When x approaches -1 from the left, the graph tends toward +infinity. When x approaches -1 from the right, the graph approaches -infinity. When it approaches 0 from both sides, the graph approaches + infinity. (Just as Alan has said.) Note that as x moves toward larger positive and negative values, it approaches y = 0. Thus, this graph has no numerical mins or max's.
+33661 When x = 0 the function goes to +∞ (the maximum). When x tends to -1 from x>-1 the function goes to -∞ (the minimum). (When x tends to -1 from x<-1 the function goes to +∞).
+33661 The minimum can only be -∞ and the maximum +∞
(I assumed k was positive in my original answer, but positive or negative the max/min are still +∞/-∞)
+130511 Here's a closer look at a "split" graph of this......I have chosen to let "k" = 1, but it's value really doesn't have any effect on the end behavior.....
Note that because of the one denominator of "x" and the other of (x+1) that this graph will have vertical asymptotes at x =0 and x = -1 (as expected). When x approaches -1 from the left, the graph tends toward +infinity. When x approaches -1 from the right, the graph approaches -infinity. When it approaches 0 from both sides, the graph approaches + infinity. (Just as Alan has said.) Note that as x moves toward larger positive and negative values, it approaches y = 0. Thus, this graph has no numerical mins or max's.
