Question

What is the domain and range of `y = 3/x`?

Answer 1

See below.

Explanation:

Domain: you shall not divide by zero: `RR - {0}`

Image: by the hyperbola graph, `RR - {0}`

Answer 2

Domain: `(-oo, 0)uu(0, +oo)`
Range: `(-oo, +oo)`

Explanation:

`y = 3/x`

`y` is defined `forall x in RR: x!=0`

Hence the domain of `y` is `(-oo, 0)uu(0, +oo)`

Now consider:

`lim_"x->0-"y =-oo`

and

`lim_"x->0+"y =+oo`

Hence the range of `y` is `(-oo, +oo)`

This can be seen from the graph of `y` below.

graph{3/x [-10, 10, -5, 5]}