Explain how to determine the end behaviour of a polynomial function. PLEASE HELP!!!?

Answer 1

http://www.purplemath.com/modules/polyends.htm

Answer 2

James L has already answered this, but just in case you find that answer a bit heavy, here are a couple of examples to show you what it means:

1. 3x^3 - 10x^2 + ... (doesn't matter what the terms with lower powers are -- when x gets big enough they don't matter much).
What sort of value does this have when x is very large?
e.g. if x = 1000, the first term is 3000000000 and the second one is -10000000, and when youvadd them together getting
2990000000 you can see that only the first term really counts, so for large positive values it will always be positive. In the same way, if you think about x = -1000 you can see that it's negative for large negative values of x.

2. -2x^5 - 8x^4 + .. (doesn't matter). Again, for large values of x the first term is the only one that matters, and so for large positive x the polynomial has negative values, for large negative x the values are positive. So if you drew a graph of this polynomial it would go off on the left into the second quadrant (upper left) and on the right into the fourth quadrant (lower right).

3. 5x^4 - 8x^3 + ... Whether x is positive or negative the first term is positive, so for large x the polynomial is positive, so its graph goes off to upper left and upper right.

4. -5x^4 -8x^3 + ... Same as previous example except that the first term is negative, so the polynomial is negative for large x (either + or -), and its graph goes off to lower left and lower right.

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Answer 3

You look at two things: the degree of the polynomial (the highest power of the variable) and the leading coefficient (associated with that highest power).

Notation: let the polynomial be defined by

y = a_n*x^n + a_n*x^(n-1) + ... + a_1 x + a_0.

Then n is the degree, and the leading coefficient is a_n. For example, if y=3x^2 + 2x + 1, then n=2 and the leading coefficient is a_2 = 3.

If n is even:

If a_n > 0, then y -> +infinity as x -> +infinity or -infinity.
If a_n < 0, then y -> -infinity as x -> +infinity or -infinity.

If n is odd:

If a_n > 0, then y -> +infinity as x -> +infinity, and
y -> -infinity as x -> -infinity.

If a_n < 0, then y -> -infinity as x-> +infinity, and
y -> +infinity as x -> -infinity

Answer 4

the question is too vague. give more detail and i probably can answer it