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

Mar 18, 2018

See explanation.

#### Explanation:

The domain of a function is the largest subset of real numbers ($\mathbb{R}$), for which the function's value can be calculated.

In the example value can be calculated for every $x \ne 0$. If $x = 0$ then you would have to divide by zero, which is not defined. Therfore the domain is: $D = \mathbb{R} - \left\{0\right\}$.

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 $+ \infty$. On the other hand if $x$ is a negative value close to zero, then the function's value goes to $- \infty$, 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]}