AP Precalculus Practice Test (2026)

Which of the following functions is a polynomial function?

Which of the following functions is a rational function?

If a polynomial function P(x) has zeros at x = -2, x = 1, and x = 3, which of the following must be a factor of P(x)?

Which of the following expressions is equivalent to (x - 3)(x + 2)^2?

A civil-engineering intern is studying how the cross-sectional profile of a newly-poured concrete drainage channel bows under load. Letting x denote the horizontal distance in meters measured from the left wall of a three-meter-wide test section, the downward deflection of the channel floor (in millimeters) is modeled by the polynomial function f(x) = x^2 - 3x + 2. The intern's supervisor asks for a single number describing how quickly the deflection changes, on average, as a sensor carriage moves from the position x = 1 to the position x = 4 along the channel.

Using the deflection model above, what is the average rate of change of f(x) over the interval [1, 4]?

Which of the following describes the end behavior of the polynomial function P(x) = -2x^5 + 3x^4 - x + 7?

What are the zeros and their multiplicities for the polynomial function f(x) = (x + 4)^3 (x - 1)^2 (x - 5)?

What are the equations of the vertical asymptotes for the rational function f(x) = (x - 3) / (x^2 - x - 6)?

Determine the equation of the slant asymptote for the rational function f(x) = (x^3 - 4x^2 + 2x - 1) / (x^2 - x + 1).

For the rational function f(x) = (x^2 - 9) / (x^2 - 2x - 3), which of the following describes any holes in the graph?

A graphics-software developer is prototyping a 'terrain sculpt' tool that lets users deform a landscape shaped like the parent cubic f(x) = x^3 by adjusting four sliders: a vertical flip, a vertical stretch factor, a horizontal translation, and a vertical translation. After the user drags the sliders and accepts the preview, the debug log for the current session reads, verbatim: 'parent = x^3; transformed g(x) = -2(x + 1)^3 + 5.' The developer now wants to describe, in plain English, every geometric operation that carried the original terrain curve f into the transformed terrain curve g — in the order produced by standard function-transformation rules.

Which of the following statements best describes the sequence of transformations applied to f(x) = x^3 to obtain g(x) = -2(x + 1)^3 + 5?

A graph of a polynomial function f(x) is shown. The graph crosses the x-axis at x = -3, touches the x-axis at x = 1, and crosses the x-axis again at x = 4. The graph rises to the left and falls to the right.

Which of the following statements about the polynomial function f(x) is true?

Consider the following table of values for a polynomial function P(x): x | P(x) --|----- -2| -10 -1| 0 0 | 2 1 | 0 2 | -2 3 | 0 4 | 10

Based on the table, which of the following statements about the polynomial function P(x) is true?

The graph of a parent function f(x) is stretched vertically by a factor of 3, reflected across the y-axis, and then shifted 2 units to the right and 4 units down.

Which of the following equations represents the transformed function g(x) in terms of f(x)?

A graph of a rational function h(x) is shown. It has a vertical asymptote at x = -2 and a horizontal asymptote at y = 1. There is a hole in the graph at x = 3.

Which of the following could be the equation for h(x)?

A scientist is studying the population growth of a certain bacteria in a petri dish. The population P (in thousands) is measured at various times t (in hours): t (hours) | P (thousands) ----------|--------------- 0 | 10 1 | 15 2 | 22 3 | 31 4 | 42 5 | 55

Based on the data, which type of function would be most appropriate to model the bacteria population P(t)?

Consider the function f(x) = (x^2 - 4x + 3) / (x^2 - 1). Which of the following statements is true regarding the discontinuities of f(x)?