Answer
The complete statement is: The behavior of the graph of a polynomial function to the far left or the far right is called its end behavior, which depends upon the leading term.
Work Step by Step
Consider the polynomial function:
$f\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+...+{{a}_{1}}x+{{a}_{0}}\left( {{a}_{n}}\ne 0 \right)$
In it, ${{a}_{n}}$ is called the leading term.
The Leading Coefficient Test: Consider the polynomial function, $f\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+...+{{a}_{1}}x+{{a}_{0}}\left( {{a}_{n}}\ne 0 \right)$, the leading coefficient is ${{a}_{n}}$.
That is, the odd-degree polynomial functions have graphs with opposite behavior at each end while even-degree polynomials show the same behavior at each end.
Therefore, from the leading coefficient test, the end behavior is governed with the help of the leading coefficients.
Hence, the behavior of the graph of a polynomial function to the far left or the far right is called its end behavior, which depends upon the leading term.
