When looking at a rational function, Charles and Bobby have two different thoughts. Charles says that the function is defined at x = –2, x = 3, and x = 5. Bobby says that the function is undefined at those x values. Describe a situation where Charles is correct, and describe a situation where Bobby is correct. Is it possible for a situation to exist where they are both correct? Justify your reasoning.

Question

vera_ewing · Answer

@freckles Do you know how to do this one?

freckles · Answer

for undefined I think it is easiest to think about vertical asymptotes or holes

freckles · Answer

Like f(x)=x-3 exists everywhere
f(3)=3-3=0

but g(x)=1/(x-3) exists everywhere but at x=3
sincve g(3)=1/0 which is not defined 
there is a vertical asymptote at x=3

freckles · Answer

we can also look at hole instead of va if you wish
h(x)=(x-3)/(x-3) doesn't exist at x=3 because the bottom would be 0 at x=3
but instead of there being a vertical asymptote at x=3
we have a hole at x=3 since (x-3)/(x-3)=1 when x isn't 3
h(x)=1 when x isn't 3

vera_ewing · Answer

So now we have to describe a situation where Charles is correct, and describe a situation where Bobby is correct. and then say if it is it possible for a situation to exist where they are both correct? Justify your reasoning.

freckles · Answer

I think you can now describe a way where charles is correct
and also a way where bobby is right

but you can't have that that a number is defined and not defined
it is either defined or undefined but never both

vera_ewing · Answer

I'm not sure how to answer the question. Can you help explain what it would be?

freckles · Answer

can  you tell me what you don't understand above in what I wrote?

freckles · Answer

like can you tell me where this function is undefined?
$$f(x)=\frac{1}{(x-4)(x-6)(x+6)}$$

freckles · Answer

what numbers can you not plug into the bottom?

vera_ewing · Answer

I just don't get how to describe a situation where Charles is correct, and describe a situation where Bobby is correct.

vera_ewing · Answer

First, what would be a situation where Charles is correct?
Then, what would be a situation where Bobby is correct?

freckles · Answer

can you answer my question please?

vera_ewing · Answer

Oh well I guess you can't plug in 0 to the bottom?

freckles · Answer

well zero is perfectly fine the plug into my function because the bottom will not be zero when replacing x with zero

freckles · Answer

when is x-4 equal to 0?
when is x+6 equal to 0?
when is x-6 equal to 0?

vera_ewing · Answer

Oh gosh I don't know... I'm sorry I'm so confused :(

freckles · Answer

x-4=0
I know you can solve this equation

freckles · Answer

even if you can't solve it I bet you should be able to give me a number that when you take 4 from it you get 0

vera_ewing · Answer

Wait so is that it? Like is that what I would say for the answer?

freckles · Answer

I don't get what your asking 
what is it?

freckles · Answer

$$f(x)=\frac{1}{(x-4)(x+6)(x-6)} \text{ is undefined at } x=4,-6,6 $$
because all of these at one point make the bottom 0

vera_ewing · Answer

How do I answer the question? Can you tell me what I would say for my answer?

freckles · Answer

do you not see that 4-4=0 and -6+6=0 and 6-6=0?

vera_ewing · Answer

No I get that, I just need to know what to say for my answer, that's all.

freckles · Answer

like if x=4 you get f(4)=1/0 which is not defined

freckles · Answer

so you can now describe a situation where bobby is right ?

freckles · Answer

just make up a function that is undefined at the values you listed in your question

vera_ewing · Answer

Can you show me?

freckles · Answer

I tried above.

freckles · Answer

I gave you an example

vera_ewing · Answer

Oh ok sorry I didn't see that. I get it now. Thanks! :)