Identify the function type
Determine the highest-degree term or dominant term
Compare degrees if the function is a rational function
Use leading coefficient and degree for polynomials
Check limits as x approaches infinity and negative infinity
Evaluate how the dominant term behaves for large positive and negative x
Determine whether the function rises or falls on each end
For rational functions, compare degrees of numerator and denominator
For exponential functions, use growth or decay behavior
For logarithmic functions, identify domain limits and asymptotic behavior
For piecewise functions, analyze each piece separately
Sketch the graph if needed to confirm the end behavior