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AP Precalc Unit 3 FRQ

The document presents a mathematical exercise involving polynomial functions and their transformations. It includes a table of values for a function 𝑓, definitions of functions ℎ and 𝑗, and asks for specific evaluations and analyses of these functions. Additionally, it prompts the reader to determine the best model for 𝑓 based on its output values.

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Jayden Savarinathan
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37 views1 page

AP Precalc Unit 3 FRQ

The document presents a mathematical exercise involving polynomial functions and their transformations. It includes a table of values for a function 𝑓, definitions of functions ℎ and 𝑗, and asks for specific evaluations and analyses of these functions. Additionally, it prompts the reader to determine the best model for 𝑓 based on its output values.

Uploaded by

Jayden Savarinathan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Unit 3: 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 ! in the table such that ℎ(𝑥) = −3, or indicate there are no such values.
(ii) Determine the end behavior of ! as ! 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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