How do you find the important parts of the equation to graph the function #y = -2/x#?

1 Answer
May 26, 2018

Domain, Range, Monotonocity.

Explanation:

  • Domain:
    In in the equation #y=-2/x#, #x!=0#
    So, Domain will be #x in RR-{0}#
  • Range:
    Given equation will give all the values except #0#
    So, Range of the function will be #y in RR-{0}#
  • Monotonocity:
    For checking increase and decrease of the function we have to derivatives of the function.
    #dy/dx=2/x^2#
    It is clear that #dy/dx>=0##AA x in RR#
    There will be discontinuity at #x=0#.
    #(d^2y)/dy^2=-4/x^3#
    So, by second derivative test,
    The graph will be concave upward for #x<0#and The graph will be concave downward for #x>0#.

So, we will be able to draw tentative sketch of the graph. The graph will be-
graph{-2/x [-10, 10, -5, 5]}