OK, so suppose we don't have the graph of a function to look at like in the last section...
Can we still find the domain and range?
Domains: 
Yes (as long as the algebra
doesn't get too hairy... and it won't for us.) 
Ranges: 
Not really (you usually need the
picture  unless it's something really basic.) 
So, we'll just be doing domains on these  which is really where the action is anyway.
Asking for the domain of a function is the same as asking
"What are all the
possible x
guys
that I can stick into this thing?"
Sometimes, what you'll really be looking for is
"Is there anything I CAN'T stick in?"
Check it out:
Let's find the domain of 
Do you see any x guys that would cause a problem here?
What about  ? 
So, x = 3 is a bad guy! Everyone else is OK, though.
The domain is all real numbers except 3.
What would the interval notation be?
When in doubt, graph it on a number line:
Do the interval notation in two pieces:
domain 
YOUR TURN:
Find the domain of 
Sometimes, you can't find the domain with a quick look.
Check it out:
Let's find the domain of 
Hmm... It's not so obvious!
BUT, we are still looking for the same thing:
The bad
x
that makes the denominator 0! 
How do we find it? Easy!
Set the denominator = 0 and solve!
The domain is 
TRY IT:
Find the domain of  *show work!! 
How about this one?
Square roots  what do we know about square roots?
... So, 16 is OK to put in.
... So, 0 is OK.
... Yuck! But, 3.2 is OK.
... Nope! Can't do it!
*We only want real numbers!
No negatives are OK!
The inside of a radical cannot be negative if we want real answers only (no i guys). So, the inside of a radical has to be 0 or a positive number.
Set  and solve it! 
Now, let's find the domain of
So, the domain of  is  . 
TRY IT:
Find the domain of  . *Show work!! 
Here's a messier one:
Let's find the domain of 
Set 

and solve! 
The domain is  . 
YOUR TURN:
Find the domain of  . *Show work! 