Question

Polynomial function P is the sum of two polynomial functions, one with degree 2 and a positive leading coefficient and one with degree 3 and a negative leading coefficient. Describe the end behavior of P. Write an example equation of two polynomial functions and their sum, P, to justify your description.

Answer 1

Answer:

As x tends to +∞, P tends to 0 and as x tends to -∞, P tends to 0.

Step-by-step explanation:

Let $f(x) = ax^{2} + bx + c$ and $g(x) = - dx^{3} + ex^{2} + fx + g$, where a, b, c, d, e, f, g all are positive coefficients.

So, the function f(x) has degree two and positive leading coefficient and g(x) has degree three and negative leading coefficient.

Now, let $P = f(x) + g(x) = - dx^{3} + (a + e)x^{2} + (b + f)x + (c + g)$

Therefore, as x tends to +∞, P tends to 0 and as x tends to -∞, P tends to 0. (Answer)