## gjhfdfg 2 years ago Leading coefficient test?

1. gjhfdfg

I have a question that wants me to use the leading coefficient test to determine the end behavior of f(x) = x^2(x + 2)

2. amistre64

expand the product to a bunch of terms that are added together

3. amistre64

then forget the stuff after the first term; the end behaviours of the function act in the same manner as the leading term

4. gjhfdfg

What do you mean?

5. amistre64

|dw:1360618376605:dw| the end behaviours of both sketches is the same .... they both behave like x^2

6. gjhfdfg

I mean what did you mean by expand the product to abunch of terms added together ?

7. amistre64

what does: x^2(x + 2) look like after you multiply the x^2 into the (x+2) ??

8. gjhfdfg

2x^23?

9. gjhfdfg

I mean 2x^3?

10. amistre64

close: x^2(x+2) = x^3 + 2x^2 now, end behaviour is what the graph acts like for values of x that go way off to the left or right zero. would you agree that the 2x^2 term contributes very little to the equation for say x=1000000000000 ?? if so, then the end bahviours (the behaviour of large values of x) gets dominated by the first term

11. gjhfdfg

I'm not sure, I wouldnt think so?

12. amistre64

the leading term of a polynomial always takes control for larger values of x. so we can know what the end behaviour of a graph of any given polynomial is by just comparing it to the standard graph of its leading term. How do the ends of x^3 behave?

13. gjhfdfg

I have no idea, I don't get any this.

14. amistre64

you need to be able to know a few basic graph shapes :/ |dw:1360619317867:dw|

15. amistre64

since the leading term of the expanded product is x^3; the ends will act in the same manner is x^3 .... another thing to keep in mind is that all even powers act alike; and all odd powers act aloike

16. gjhfdfg

Thanks for trying to explain this to me, I think Im just gonna have to find me a tutor. Problems like this is foreign language to me, very hard to under stand.