2025 AP Precalculus Free-Response Questions

1. The function f is decreasing and is defined for all real numbers. The table gives values for f(x) at selected values of x. | x | -2 | -1 | 0 | 1 | 2 | |---|---:|---:|---:|---:|---:| | f(x) | 14 | 7 | 3.5 | 1.75 | 0.875 | The function g is given by g(x) = −0.167x³ + x² − 1.834. A. i. The function h is defined by h(x) = (g ∘ f)(x) = g(f(x)). Find the value of h(1) as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer. ii. Find the value of f⁻¹(3.5), or indicate that it is not defined. B. i. Find all values of x, as decimal approximations, for which g(x) = 0, or indicate that there are no such values. ii. Determine the end behavior of g as x increases without bound. Express your answer using the mathematical notation of a limit. C. i. Based on the table, which of the following function types best models function f: linear, quadratic, exponential, or logarithmic? ii. Give a reason for your answer in part C (i) based on the relationship between the change in the output values of f and the change in the input values of f. Refer to the values in the table in your reasoning.