indicate whether the following statement is true or false. odd - degree polynomial functions have graphs…

indicate whether the following statement is true or false. odd - degree polynomial functions have graphs with opposite behavior at each end. fill in the blank below. the statement is

indicate whether the following statement is true or false. odd - degree polynomial functions have graphs with opposite behavior at each end. fill in the blank below. the statement is

Answer

Explanation:

Step1: Recall the end - behavior of polynomial functions

For a polynomial function (f(x)=a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0), where (n) is a non - negative integer and (a_n\neq0). The end - behavior is determined by the leading term (y = a_nx^n). When (n) is odd: If (a_n>0), as (x\rightarrow\infty), (y = a_nx^n\rightarrow\infty) and as (x\rightarrow-\infty), (y=a_nx^n\rightarrow-\infty). If (a_n < 0), as (x\rightarrow\infty), (y=a_nx^n\rightarrow-\infty) and as (x\rightarrow-\infty), (y = a_nx^n\rightarrow\infty).

Answer:

The statement is True.