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

1 Answer
Mar 18, 2018

Answer:

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]}