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AP Precalc Unit 3 FRQ

The document provides a table of x and f(x) values and defines several functions based on f(x) and another function g(x). It then asks questions about evaluating the defined functions at given values, determining values of x where another function is equal to a given value, finding the end behavior of g(x), and determining the best fitting polynomial model for f(x) based on its table of values.

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Maximilian Shabatayev
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3K views1 page

AP Precalc Unit 3 FRQ

The document provides a table of x and f(x) values and defines several functions based on f(x) and another function g(x). It then asks questions about evaluating the defined functions at given values, determining values of x where another function is equal to a given value, finding the end behavior of g(x), and determining the best fitting polynomial model for f(x) based on its table of values.

Uploaded by

Maximilian Shabatayev
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Graphing Calculator Allowed

𝑥 −2 −1 0 1 2 3 4 5
𝑓(𝑥) −26 −10 −4 −2 2 14 40 86

Let 𝑓 be a polynomial function defined for all 𝑥. The table gives values of 𝑓(𝑥) at selected values of
𝑥. The function 𝑔 is given by 𝑔(𝑥) = 𝑥 ! − 5𝑥 + 4.

(A) (i) The function ℎ is defined by ℎ(𝑥) = 𝑓(3𝑥 + 6) + 1. Find the value of ℎ(−1).
(ii) The function 𝑗 is defined by 𝑗(𝑥) = 3𝑔(2𝑥 − 5) − 4. Find the value of 𝑗(2).

(B) (i) Find all values of x in the table such that ℎ(𝑥) = −3, or indicate there are no such values.
(ii) Determine the end behavior of g as x decreases without bound. Express your answer using
the mathematical notation of a limit.

(C) (i) Use the table of values for 𝑓 to determine if 𝑓 is best modeled by a linear, quadratic, cubic, or
quartic function.
(ii) Give a reason for your answer based on how the output values of 𝑓 change with respect to
the input values of 𝑓.

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