Question

How do you find the domain and range for `y = 1/x`?

Answer 1

See explanation.

Explanation:

The domain of a function is the largest subset of real numbers (`RR`), for which the function's value can be calculated.

In the example value can be calculated for every `x!=0`. If `x=0` then you would have to divide by zero, which is not defined. Therfore the domain is: `D=RR-{0}`.

The range is set of all values `y` which the function takes.

Here we can say that if `x` is a positive value close to zero the value of function rises to `+oo`. On the other hand if `x` is a negative value close to zero, then the function's value goes to `-oo`, so the range is:

`r=(-oo;0)uu(0;+oo)`

We can see both range and domain in the graph:

graph{1/x [-10, 10, -5, 5]}