AP Precalculus Polynomial Functions

Question 1

What is the end behavior of f(x) = −2x⁵ + 3x² − 1?

Accepted Answer

f(x) → −∞ as x → ∞ and f(x) → ∞ as x → −∞

Answer

The leading term −2x⁵ has odd degree and a negative coefficient, so the graph falls to the right and rises to the left.

Question 2

What is the average rate of change of f(x) = x² − 4x + 1 over the interval [1, 5]?

Accepted Answer

2

Answer

f(5) = 6 and f(1) = −2, so the average rate of change is (6 − (−2))/(5 − 1) = 2.

Question 3

A quadratic function has average rates of change of 3 on [0, 1] and 7 on [1, 2]. If this pattern continues, what is its average rate of change on [2, 3]?

Accepted Answer

11

Answer

For a quadratic, average rates of change over consecutive equal-length intervals change by a constant amount; here it increases by 4, so the next value is 11.

Question 4

Which is a polynomial of least degree with real coefficients that has 2 and 1 + i as zeros?

Accepted Answer

x³ − 4x² + 6x − 4

Answer

Complex zeros of real-coefficient polynomials come in conjugate pairs, so 1 − i is also a zero, and (x − 2)(x² − 2x + 2) = x³ − 4x² + 6x − 4.

Question 5

The point (4, 5) lies on the graph of y = f(x). Which point must lie on the graph of g(x) = −f(x − 3) + 2?

Accepted Answer

(7, −3)

Answer

Replacing x with x − 3 shifts the graph right 3, giving x = 7; the negative reflects the y-value to −5 and +2 raises it to −3.

AP Precalculus Practice Test

AP Precalculus Practice Test

AP Precalculus Polynomial Functions