Which term describes the behavior of the graph of a function as x approaches positive infinity or negative infinity?

• A. End Behavior
• B. Similar
• C. Rational
• D. Irrational

Answer: (A)

End behavior is the way a graph behaves as x goes to positive or negative infinity. This term captures what the function does far out on the right and far out on the left, regardless of what happens in between. For polynomials, the end behavior is driven by the leading term, so as x grows large in magnitude, the graph follows the highest-degree term: ends rise or fall depending on the degree's parity and the leading coefficient; for example, even degree with a positive leading coefficient sends both ends upward, while odd degree can send one end up and the other down. For rational functions, end behavior is analyzed by comparing the degrees of the numerator and denominator to predict horizontal or oblique ends. The other terms don’t describe this specific asymptotic behavior: they refer to different ideas such as the nature or type of the function, not what happens as x becomes very large in either direction.