Heinz boasts that he can predict the degree of a polynomial function just by looking at the end behavior. Can Heinz do this? Explain.

Question

anonymous · Answer

1'm pretty sure he can't but 1 don't know why.

anonymous · Answer

@freckles @tkhunny

tkhunny · Answer

It can be narrowed down to Odd or Even.

"Predict" is not a good word for this problem.

anonymous · Answer

anything else?

mathteacher1729 · Answer

This is also assuming your graphing window reveals the true end behavior of the polynomial. (see attached gif)

anonymous · Answer

but WHY can't he determine the degree?

mathteacher1729 · Answer

http://www.purplemath.com/modules/polyends.htm has some useful information about polynomial end behavior. Basically all you can know (assuming your window reveals the correct end behavior) is whether the polynomial is even or odd and whether the leading coefficient is + or -. Even if you knew the roots of the polynomial from the graph, that doesn't say anything about possible complex roots or repeated roots. Also how accurate is the graph we're looking at? I'm not sure how open ended your question is, but if you know correct end behavior all you can say is the two things I've mentioned before. :) I suggest going to desmos.com/calculator and graphing a bunch of polynomials of varying degrees to see why this is so, then state those results in your own words. You can also ask your teacher for clarification about the question.

tkhunny · Answer

We should assume the true end behavior, because the problem statement told us so.

Heinz can know the parity (odd or even) of the degree from the true end behavior because there are two and only two possible outcomes for polynomials.  You should find this in your discover suggested by mathteacher1729.