Question

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

Answer 1

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]}