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

May 26, 2018

Domain, Range, Monotonocity.

#### Explanation:

• Domain:
In in the equation $y = - \frac{2}{x}$, $x \ne 0$
So, Domain will be $x \in \mathbb{R} - \left\{0\right\}$
• Range:
Given equation will give all the values except $0$
So, Range of the function will be $y \in \mathbb{R} - \left\{0\right\}$
• Monotonocity:
For checking increase and decrease of the function we have to derivatives of the function.
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2}{x} ^ 2$
It is clear that $\frac{\mathrm{dy}}{\mathrm{dx}} \ge 0$$\forall x \in \mathbb{R}$
There will be discontinuity at $x = 0$.
$\frac{{d}^{2} y}{\mathrm{dy}} ^ 2 = - \frac{4}{x} ^ 3$
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]}