Answer
The given statement is true.
Work Step by Step
Let us consider a polynomial $f\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+\cdots +{{a}_{0}}$.
It is know that the behavior of the function to the far left or the far right is called its end behavior.
The end behavior of the graph of the polynomial depends on the coefficient of the term having the highest power; this coefficient is called the leading coefficient or the leading term.
Now, the degree of the polynomial is n; if n is odd then the cases are as follows:
Case I: $a>0$
In case there is a positive value for the leading coefficient, the graph falls to the left side and rises to the right side.
Case II: $a<0$
In case there is a negative value for the leading coefficient, the graph rises to the left side and falls to the right side.
Thus, we can see that when the degree of the polynomial is odd the graph has opposite behavior at the ends.
Therefore, the given statement is true.
