# What is the domain and range of #y= 1 / (x-3) #?

##### 1 Answer

Domain:

Range:

#### Explanation:

You can't divide by zero, meaning the denominator of the fraction cannot be zero, so

Thus, the domain of the equation is

Alternately, to find the domain and range, look at a graph:

graph{1/(x-3) [-10, 10, -5, 5]}

As you can see, the x never equals 3, there is a gap at that point, so the domain doesn't include 3 - and there is a vertical gap in the range of the graph at y=0, so the range doesn't include 0.

So, again, the domain is

And the range is

NOTE: Another way to find y that may or may not be allowed (solving for x):

Multiply both sides by x:

Divide by y:

Add 3:

Since you can't divide by zero,