Identify the function type
Look at the highest-degree term for polynomials
Use the leading coefficient and degree
For even degree, both ends go in the same direction
For odd degree, the ends go in opposite directions
For positive leading coefficient, the right end rises
For negative leading coefficient, the right end falls
For rational functions, compare the degrees of numerator and denominator
If numerator degree is less than denominator degree, both ends approach 0
If numerator degree equals denominator degree, both ends approach the ratio of leading coefficients
If numerator degree is greater than denominator degree, use long division or asymptotic behavior
Check limits as x approaches positive infinity and negative infinity
Use graphing or a table if needed to confirm behavior