2024 AP Precalculus Free-Response Questions
Advanced PlacementAP PrecalculusFree ResponseMathematics
4 questions24 pts
4 gradable24 rubric criteria0 dependencies
q1Question 1
q1
Question 1
The figure shows the graph of the function f on its domain of −3.5 ≤ x ≤ 3.5. The points (−3, 1), (0, 1), and (3, 1) are on the graph of f. The function g is given by g(x) = 2.916 · (0.7)^x. (A) (i) The function h is defined by h(x) = (g ∘ f)(x) = g(f(x)). Find the value of h(3) as a decimal approximation, or indicate that it is not defined. (ii) Find all values of x for which f(x) = 1, or indicate that there are no such values. (B) (i) Find all values of x, as decimal approximations, for which g(x) = 2, 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) Determine if f has an inverse function. (ii) Give a reason for your answer based on the definition of a function and the graph of y = f(x).
Rubric Criteria (6)
q1_A_iThe response gives h(3)=2.041 as a decimal approximation, correct to three decimal places by rounding or truncating. The first decimal-presentation error in Question 1 makes this point ineligible.
1.0000pts
q1_A_iiThe response identifies exactly x=-3, x=0, and x=3 as all values for which f(x)=1, with no incorrect values included. Supporting work is not required.
1.0000pts
q1_B_iThe response gives x=1.057 as the solution to g(x)=2, expressed as a decimal approximation correct to three decimal places, with no incorrect values included. The first decimal-presentation error in Question 1 makes this point ineligible.
1.0000pts
q1_B_iiThe response states the end behavior using a limit that includes all four required components: lim, x→∞, the function g, and 0; equivalently, lim_{x→∞}g(x)=0. If an additional complete limit statement is included, it must also be correct.
1.0000pts
q1_C_iThe response states that f does not have an inverse function on its domain −3.5≤x≤3.5.
1.0000pts
q1_C_iiThe response explains, with an implicit or explicit reference to the definition of a function, that f has output values not mapped from unique input values, and supports this with specific function values such as f(−3)=f(0)=f(3)=1. This criterion cannot be awarded if Part (C)(ii) contains an error.
1.0000pts
Dependencies (0)
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