How do you find the domain of #y = 3/x#?

1 Answer

Answer:

#x!=0#

Explanation:

The Domain is the list of allowable values of #x#. I find it easiest to first say #x# is all values and then find any that #x# can't be. So - are there any values that #x# can't be?

The answer is yes: #x!=0# because that would make the fraction divisible by 0 and that is a no-no.

We can express this in a few different ways. One way is to simply write #x!=0#. Another is to write #(-oo,0), (0,oo)#. And there are others that have more rigorous notation.

Here's a graph to see the disallowed value of #x#:

graph{3/x[-10,10,-100,100]}