the end behavior of a polynomial function is determined by the degree and the sign of the leading…

the end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient. identify the degree of the polynomial and the sign of the leading coefficient leading coefficient positive; degree - even leading coefficient positive; degree - odd leading coefficient negative; degree - even leading coefficient negative; degree - odd

the end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient. identify the degree of the polynomial and the sign of the leading coefficient leading coefficient positive; degree - even leading coefficient positive; degree - odd leading coefficient negative; degree - even leading coefficient negative; degree - odd

Answer

Explanation:

Step1: Recall end - behavior rules

For a polynomial (y = a_nx^n+\cdots+a_0), if (n) (degree) is even: when (a_n>0), as (x\to\pm\infty), (y\to+\infty); when (a_n < 0), as (x\to\pm\infty), (y\to-\infty). If (n) (degree) is odd: when (a_n>0), as (x\to+\infty), (y\to+\infty) and as (x\to-\infty), (y\to-\infty); when (a_n < 0), as (x\to+\infty), (y\to-\infty) and as (x\to-\infty), (y\to+\infty).

Step2: Analyze the graph

In the given graph, as (x\to+\infty), (y\to-\infty) and as (x\to-\infty), (y\to-\infty). This is the case when the degree (n) is even (because the ends of the graph go in the same direction) and the leading coefficient (a_n<0) (since the graph is "down - ward" on both ends).

Answer:

Leading Coefficient Negative; Degree - Even