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?

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:

Do you see any x guys that would cause a problem here?

 

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:

 

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YOUR TURN:

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Sometimes, you can't find the domain with a quick look.

Check it out:

Hmm...  It's not so obvious!

BUT, we are still looking for the same thing:

How do we find it?  Easy!

Set the denominator = 0 and solve!

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TRY IT:

 

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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.

Now, let's find the domain of

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TRY IT:

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Here's a messier one:

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YOUR TURN:

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