# What is the domain and range of #(x+5)/(x+1)#?

##### 1 Answer

Domain =

Range =

#### Explanation:

First of all, we must note that this is a reciprocal funtion, as it has

The division by zero is not defined in mathematics, so this function will not hava a value associated to

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

There is also a hidden range restriction in this function. Notice that the curves will keep going towards the infinitity in both sides by the x axis, but they never reach a value. We must calculate the limits of the function in both infinities:

This number can be found if you solve the function for a very big number in x (1 million, for example) and a very small number (-1 million). The funcion will get near

Finally, the domain can be any number, except -1, so we write it this way:

The range can be any number except 1: #RR-{1}.