The behavior of the graph of a polynomial function to

Explanation
Consider the polynomial function
${\displaystyle f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0(a_n\ne 0)}$
In it ${\displaystyle a_n}$ is called the leading term.
The leading coefficient test:
Consider the polynomial function, ${\displaystyle f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0(a_n\ne 0)}$
That is leading coefficient is an. then,
For n is odd
${\displaystyle \left(a\right)a_n>0}$, the graph falls to the left and rises to the right.
${\displaystyle \left(a\right)a_n<0}$, the graph rises to the left and falls to the right
For n is even
${\displaystyle \left(a\right)a_n>0}$, the graph rises to the left and rises to the right.
${\displaystyle \left(a\right)a_n<0}$, the graph falls to the left and falls to the right.
Step 2
That is, Odd-degree polynomial function have graphs with opposite behavior at each end while even-degree polynomial shows 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.