Question

graphing reciprocal functions:

f(x)=- 3/(x+1) -2

Answer 1

Okay, where do you plan to start? I would recommend obvious stuff, first.

Answer 2

i just need to figure out the domain.

Answer 3

That IS the most obvious piece. It's kind of staring at you in this form. Once you see how to get it, you be delighted at how easy the next problem is.

Typically, we start Domain research by simply assuming All Real Numbers. Then we hunt around for things we have to throw out. Take a look at that denominator. (x+1) What would happen at x = -1?

Answer 4

would it just cancel?

Answer 5

or become a positive number?

Answer 6

Think about it a little longer.

Here we have an expression: \(\dfrac{3}{x+1}\).

What is the value of the expression for x = -1?

Answer 7

-1

Answer 8

No. You are not interpreting the result correctly. It is unusual. I am glad that you are trying to see what it is, but so far, you haven't landed in the right place.

If x = -1, we have \(\dfrac{3}{-1+1} = \dfrac{3}{0}\). Does that even mean anything?!

Answer 9

ok yes

Answer 10

Yes, what? 3/0 doesn't mean anything. It's not a number.

Answer 11

ok

Answer 12

This has an important implication for the Domain. Can we use values that lead to nonsense?

Answer 13

no?

Answer 14

In this case, x = -1 is the ONLY thing we have to worry about. The rest of this guy is very well-behaved. And we have the Domain!! Can you state what it is?

Answer 15

-1 right?

Answer 16

You have the right idea, but you don't remember why we were playing with x = -1. We were playing with it to get rid of it!! We don't want to keep it.

The Domain is All Real Numbers EXCEPT x = -1. This can be expressed several ways. The easiest might be simply \(x \ne -1\). Done!

Answer 17

ok thank you!