SOLUTION: Please explain how tail behavior works. This question is really confusing me. Here's the image: http://i.imgur.com/sLruXc7.png Thank you!

Algebra ->  Permutations -> SOLUTION: Please explain how tail behavior works. This question is really confusing me. Here's the image: http://i.imgur.com/sLruXc7.png Thank you!      Log On


   

Question 933467: Please explain how tail behavior works. This question is really confusing me.
Here's the image:
http://i.imgur.com/sLruXc7.png
Thank you!
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The degree of the function or polynomial tells the shape behavior. Degree 1 is a line and has no turning point; degree 2 has one turning point; degree 3 could have up to two turning points; and degree 4 could have as many as three turning points. The number of possible turning points goes upward correspondingly according to the degree.

The sign of the coefficient of the leading term tells the left & right tail behavior. Also, the evenness or oddness of the degree tells you something about this. Both the coefficient and the degree tell what the tail behavior is. Degree odd and positive coefficient on lead term means downward to the left and upward to the right; degree odd and leading coefficient negative means tail up toward the left and tail downward to the right. Degree even and leading coefficient positive means both tails up; and degree even with lead coefficient negative means both tails downward.