AP PreCalculus Flashcards: Polynomial Functions and End Behavior
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
Is it possible for the output of a nonconstant polynomial to approach a specific number as the input increases without bound?
No, as input values increase or decrease without bound, the output values of a nonconstant polynomial must also increase or decrease without bound, not approach a finite limit.
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Is it possible for the output of a nonconstant polynomial to approach a specific number as the input increases without bound?
No, as input values increase or decrease without bound, the output values of a nonconstant polynomial must also increase or decrease without bound, not approach a finite limit.
What is the end behavior of a polynomial function?
End behavior describes how the output values of a nonconstant polynomial function behave as its input values increase or decrease without bound.
What is the 'leading term' of a polynomial?
The leading term is the term in a polynomial with the highest degree, whose value dominates all other terms for extreme input values.
Why does the leading term dictate a polynomial's end behavior?
As input values increase or decrease without bound, the values of the leading term dominate the values of all lower-degree terms, controlling the function's direction.
What two factors determine the end behavior of a polynomial function?
The degree and the sign of the leading term of a polynomial determine the end behavior of the function.
Which part of a polynomial function is least important when determining its end behavior?
The lower-degree terms and the constant term are the least important, as their values are dominated by the leading term for very large or very small input values.
What happens to the output values of a nonconstant polynomial as its input values decrease without bound?
As input values decrease without bound, the output values will either increase or decrease without bound, depending on the leading term.
If a polynomial's leading term has an even degree and a positive sign, what happens as input values decrease without bound?
The output values will increase without bound. This is determined by the properties of the degree and sign of the leading term.
What happens to the output values of a nonconstant polynomial as its input values increase without bound?
As input values increase without bound, the output values will either increase or decrease without bound, depending on the leading term.
In the context of end behavior, what does it mean for a term to 'dominate'?
Dominance means that as input values become extremely large or small, the value of the leading term becomes so much larger than all other terms that it alone determines the function's behavior.