## anonymous one year ago Describe the end behavior of each function. A. y=x^4 +5 B. Y=-x^5+5x^3-2x+3

1. misty1212

HI!!

2. misty1212

the first one has degree 4, which is even

3. misty1212

also it has a positive leading coefficient (it is 1)

4. misty1212

therefore as $$x\to \infty$$ you have $$x^4+5\to\infty$$ and as $$x\to -\infty$$ you have $$y^4+5\to \infty$$

5. misty1212

|dw:1434205740470:dw|

6. misty1212

do you know what a polynomial of odd degree with negative leading coefficient looks like?

7. anonymous

No, sorry

8. misty1212

ok lets start with a polynomial of degree 1, a line, with negative leading coefficient, like say $$y=-x+1$$ you know what that looks like?

9. anonymous

Yes

10. misty1212

it has the same "end behavior' as any polynomial of odd degree with negative leading coefficient

11. anonymous

Ok

12. misty1212

you got that? goes to positive infinity as x goes to negative infinity, and negative infinity as x goes to positive infinity

13. anonymous

So the answer is x^4+5 > infinity

14. anonymous

?

15. misty1212

do you know what "end behavior" means?

16. anonymous

Yeah

17. anonymous

Refer to the attachment

18. anonymous

both a and b are functions that have an odd number as their highest exponential degree. so the as x gets bigger, so does y. and as x gets smaller, so does y. the answer for the limit for both is |dw:1434210988972:dw| |dw:1434211163340:dw|

19. anonymous

just keep ∞ and ∞ in the same equation and -∞ and -∞ in the same equation. for both and you're all set