Question

Find the domain of the function algebraically and support your answer graphically

Answer 1

\[\frac{ 3x-1 }{ (x+3)(x-1) }\]

Answer 2

What do you mean

Answer 3

To find the domain, you would have to look at the denominator and see what X cannot equal, or else it will be undefined.

Set x+3=0
Set x-1=0

Whatever equals zero, X cannot equal. These are excluded from your domain.

Answer 4

Ok

Answer 5

I think what is meant by the "support your answer graphically" part is to show that the graph of the function has vertical asymptotes at those values of x that are not in the domain.

Answer 6

So my teach like taught us how to do it graphically with the calculator, but not algebraically. So basically you're saying that x=-3 and x=1 can not be in the domain? @dimensionx

Answer 7

Correct

Answer 8

Because you cannot have zero in the denominator.

Answer 9

so then the domain would be\[(-\infty,-4) \upsilon (2,\infty)\]

Answer 10

@dimensionx

Answer 11

How did you get that? @dimensionx told you to solve:

x+3=0
x-1=0

What do you get?

Answer 12

x=-3 and x=1

Answer 13

OK, so if you leave those two values of x out of the domain, then what do you get?

(I'm not seeing how you came up with \((-\infty,-4) \cup (2,\infty)\)??)

Answer 14

First off, you are leaving out all the values between -4 and 2.... but also, -4 and 2 aren't the values that are to be left out of the domain.

Answer 15

so it would be \[(-\infty,-3)\upsilon(1,\infty)\]

Answer 16

am i close? lol

Answer 17

OK, that's better - closer, yes! :)

But you are leaving out everything between -3 and 1. EVERYTHING except for -3 and 1 are in the domain.

Answer 18

so is it like
\[(-\infty,-3)\upsilon(-3,1)\upsilon(1,\infty)\]

Answer 19

YES, exactly like that. :) good job!

Answer 20

oh yeahhhh!!!!!!! :DDDDD so it's pretty easy lol thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! @DebbieG can i like double fan you? lol

Answer 21

lol you're welcome... happy to help :)

Answer 22

{R}-(-3)
{R}-1