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]}