Question

find the domain y = x^2-16/x^3+2x^2-9x-18. still not understanding how to do this

Answer 1

The denominator is \(x^3+2x^2-9x-18\), right?

Answer 2

What methods have you been taught for finding roots of a 3rd degree polynomial?

Graphing? Rational root theorem? Synthetic division?

Answer 3

The problem is x^2 over x^3+2x^2-9x-18. Looking for the domain.

Answer 4

sorry the first part is x^2-16 over the rest

Answer 5

Ok, so like I said - the denominator of the function is \(x^3+2x^2-9x-18\). I just wanted to confirm that since you did not use any ( ) so it can be vague in meaning.

Answer 6

OK, the numerator isn't really very relevant if we are just looking for the domain. How do you find the domain of a rational function?

Or maybe the way to ask it is: what kind of value ISN'T in the domain of a rational function?

Answer 7

E.g., for the function \(\Large y=\dfrac{ 3 }{ x-2 }\) ..... what is the domain?

Answer 8

2

Answer 9

The domain is 2?

Answer 10

No.... not exactly.....

Answer 11

everything except 2

Answer 12

RIGHT. So in general, how do you find the domain of a rational function? It's everything EXCEPT the values that............?

Answer 13

equal 0

Answer 14

Well, sort of. It's everything except the X values that make the DENOMINATOR =0. right?

Remember - domain is all about the x's. What x's are ALLOWED to be plugged into the equation. When it comes to a rational function, the x's that are NOT allowed are those that make the den'r=0.

Answer 15

So what you need to do here, if find all the x's that make this den'r=0. That is, you have to solve:

\(\Large x^3+2x^2-9x-18=0\)

Which brings me back to.... :) What methods have you been taught for finding roots of a 3rd degree polynomial?

Graphing? Rational root theorem? Synthetic division?

Answer 16

When you solve that equation, you'll know what has to be left out of the domain.

Answer 17

rational root

Answer 18

OK. so by rational root theorem, any rational root of this function (if one exists) must be a factor of what number?

Answer 19

2

Answer 20

That rational root theorem says that IF a number is rational root, then it is of the form \(\pm\)p/q, where p is a factor of the constant term (in this case, that is 18) and q is a factor of the leading coefficient (in this case, 1).

so you need to find all factors of p=18, and q=1, (so in this case, really just all factors of 18). THAT list includes any rational roots. Notice that it doesn't guarantee that there are ANY rational roots - but only that, if there ARE, they are on that list.

Answer 21

ok so i got a domain of everything except for 3,-3 and -2

Answer 22

Very good - that's it! :)

Answer 23

Thank you