Question

How do you graph `f(x)=-2/x` using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer 1

See below.

Explanation:

`y = -2/x`

`y` axis intercepts occur where `x=0`

`y= -2/(0)` Undefined (Division by zero):

`x` axis intercepts occur where `y=0`:

`0=-2/x`

Solving for `x`

`0x = -2=> 0!= -2`

No intercepts of `x` axis:

As `x-> oo`

`-2/x-> 0`

As `x->-oo`

`-2/x-> 0`

`x` axis is a horizontal asymptote.

Left hand limit:

`lim_(x->0^-)-2/x->oo`

Right hand limit:

`lim_(x->0^+)-2/x->-oo`

`y` axis is a vertical asymptote.

Graph of `y=-2/x`

graph{y=-2/x [-10, 10, -10, 10]}