G(x)=
find the domain, show work

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 off( x ) = 2 / ( x - 3 )

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

What aboutx = 3?

f( 3 ) = 2 / ( 3 - 3 ) = 2 / 0  ...  ouch!

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:

number line showing the domain is all numbers except 3

Do the interval notation in two pieces:

domain= ( -infinity , 3 ) U ( 3 , infinity )

YOUR TURN:

Find the domain off( x ) = 5 / ( x + 7 )

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

Check it out:

Let's find the domain off( x ) = 1 / ( 3 - 2x )

Hmm...  It's not so obvious!

BUT, we are still looking for the same thing:

f( x ) = 1 / ( 3 - 2x )The bad x that makes

the denominator 0!

How do we find it?  Easy!

Set the denominator = 0 and solve!

3 - 2x = 0 ... subtract 3 from both sides ... -2x = -3 ... x = -3 / -2 = 3 / 2