Answer
The given statement is true.
Work Step by Step
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 and this coefficient is known as the leading coefficient or the leading term.
The degree of the polynomial is n; if n is even then the cases are as follows:
Case I: $a>0$
In case there is a positive value for the leading coefficient, the graph rises 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 falls to the right side and falls to the left side.
Therefore, for positive and negative value of the leading term, the graph of the polynomial with even degree behaves the same at both ends.
Hence, the given statement is true.
