Identify the leading term of the polynomial
Note the degree of the leading term
Note the sign of the leading coefficient
If the degree is even and the leading coefficient is positive, both ends rise
If the degree is even and the leading coefficient is negative, both ends fall
If the degree is odd and the leading coefficient is positive, left end falls and right end rises
If the degree is odd and the leading coefficient is negative, left end rises and right end falls
Use the leading term to determine the behavior as x approaches positive infinity and negative infinity
Write the end behavior in limit notation if needed