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AP PreCalculus Practice Quiz: Polynomial Functions and End Behavior

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 10 questions to check your progress.

Question 1 of 10

According to the provided text, which two characteristics of a polynomial function are sufficient to determine its end behavior?

All Questions (10)

According to the provided text, which two characteristics of a polynomial function are sufficient to determine its end behavior?

A) The y-intercept and the number of roots

B) The degree and the sign of the leading term

C) The constant term and the degree

D) The number of terms and the sign of the constant term

Correct Answer: B

The text explicitly states that 'The degree and sign of the leading term of a polynomial determines the end behavior of the polynomial function.'

Why does the leading term of a nonconstant polynomial function have the greatest influence on its end behavior?

A) It is always the term with the largest coefficient.

B) Its values dominate the values of all lower-degree terms for inputs of large magnitude.

C) It determines the location of the function's y-intercept.

D) It is the only term that can have a negative sign.

Correct Answer: B

The provided content explains that 'as the input values increase or decrease without bound, the values of the leading term dominate the values of all lower-degree terms.'

For a nonconstant polynomial function, as the input values increase without bound, which of the following describes the possible behavior of the output values?

A) They will approach a specific constant value.

B) They will either increase or decrease without bound.

C) They will always approach zero.

D) They will oscillate between two fixed values.

Correct Answer: B

The text states, 'As input values of a nonconstant polynomial function increase without bound, the output values will either increase or decrease without bound.'

Which of the following best defines the 'end behavior' of a polynomial function?

A) The behavior of the function near its roots or x-intercepts.

B) The maximum and minimum points of the function.

C) The behavior of the function's output as the input values grow infinitely large or infinitely small.

D) The value of the function when the input is zero.

Correct Answer: C

End behavior describes how the output values of a function behave as the input values 'increase or decrease without bound,' which means they approach positive or negative infinity.

Consider the polynomial f(x) = -10x^2 + 5x^5 - 300. The end behavior of this function is determined by the properties of which term?

A) -10x^2, because it is the first term.

B) 5x^5, because it is the term with the highest degree.

C) -300, because it is the constant term.

D) All terms contribute equally to the end behavior.

Correct Answer: B

The leading term, which is the term with the highest degree, determines the end behavior. In this polynomial, the term with the highest degree is 5x^5.

Which of the following describes a behavior that is IMPOSSIBLE for the end behavior of a nonconstant polynomial function as its input values decrease without bound?

A) The output values increase without bound.

B) The output values decrease without bound.

C) The output values approach a horizontal asymptote.

D) The output values are dictated by the leading term.

Correct Answer: C

The provided text states that for a nonconstant polynomial, output values must either increase or decrease without bound as input values do. They cannot level off and approach a specific finite value, which is the definition of a horizontal asymptote.

The principle of leading term dominance explains why:

A) polynomials have smooth, continuous graphs.

B) we only need to analyze a single term to determine a polynomial's end behavior.

C) a polynomial of degree 'n' can have at most 'n' real roots.

D) the y-intercept of a polynomial is its constant term.

Correct Answer: B

The fact that the leading term's values dominate all other terms for large inputs is the reason we can simplify the analysis of end behavior to just that one term's degree and sign.

Two different nonconstant polynomial functions, P(x) and Q(x), are found to have the exact same end behavior. Based on the provided principles, which statement must be true about their leading terms?

A) Their leading terms must be identical.

B) The degrees of their leading terms must have the same parity (both even or both odd) and their leading coefficients must have the same sign.

C) Their leading coefficients must be equal in value.

D) The degrees of their leading terms must be equal.

Correct Answer: B

Since the degree and the sign of the leading coefficient together determine the end behavior, two functions with the same end behavior must have leading terms whose degree and sign combination produce that behavior. For example, 2x^4 and 5x^4 have the same end behavior because their degrees are both even and their coefficients are both positive.

In the study of polynomial functions, the phrase 'as input values decrease without bound' is a formal way of describing which condition?

A) As x approaches 0 from the left.

B) As x approaches negative infinity.

C) As x approaches a large, specific negative number.

D) As x approaches positive infinity.

Correct Answer: B

'Decreasing without bound' means that the values are becoming infinitely large in the negative direction, which is mathematically expressed as approaching negative infinity.

Which statement is a direct consequence of the principles of polynomial end behavior described in the text?

A) A nonconstant polynomial function cannot have both a maximum and a minimum value.

B) The graph of a nonconstant polynomial function cannot be a horizontal line.

C) A nonconstant polynomial function must cross the x-axis at least once.

D) The graph of a nonconstant polynomial function cannot be contained entirely within a finite rectangular area.

Correct Answer: D

Because the output values of a nonconstant polynomial must either increase or decrease without bound as x approaches positive or negative infinity, the graph must extend infinitely upwards or downwards, and thus cannot be confined to a finite area.