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📈AP Pre-Calculus
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📈AP Pre-Calculus

FRQ 1 – Function Concepts (Calculator)
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Unit 1: Polynomial and Rational Functions
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AP Precalculus FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

FRQFocusUnitsWhy
FRQ 1Function Concepts (Calculator)1-2Tests function analysis with graphing calculator - Units 1-2 polynomial/rational functions
FRQ 2Modeling a Non-Periodic Context1-2Tests modeling with polynomial, rational, exponential, or logarithmic functions
FRQ 3Modeling a Periodic Context3 onlyTests modeling with trigonometric functions - all Unit 3 content
FRQ 4Symbolic ManipulationsAllTests algebraic manipulation skills that span all units

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 21/2

1. The function fff is increasing and is defined for all real numbers. The table gives values for f(x)f(x)f(x) at selected values of xxx. The function ggg is given by g(x)=−0.2x3+1.5x2+x−4g(x) = -0.2x^3 + 1.5x^2 + x - 4g(x)=−0.2x3+1.5x2+x−4. The function hhh is defined by h(x)=(gcircf)(x)=g(f(x))h(x) = (g \\circ f)(x) = g(f(x))h(x)=(gcircf)(x)=g(f(x)).

  • g(x) = -0.2x^3 + 1.5x^2 + x - 4

  • h(x) = g(f(x))

x

f(x)

1

4

2

7

3

14

4

25

5

40

A.
i.

Find the value of h(2)h(2)h(2) 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(25)f^{-1}(25)f−1(25), or indicate that it is not defined.

B.
i.

Find all values of xxx, as decimal approximations, for which g(x)=0g(x) = 0g(x)=0, or indicate that there are no such values.

ii.

Determine the end behavior of ggg as xxx 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 fff: 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 fff and the change in the input values of fff. Refer to the values in the table in your reasoning.

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FRQ Directions
Free Response Question Practice

This practice environment simulates the AP AP Pre-Calculus Free Response Questions section. Here are some guidelines:

  • Read each question carefullybefore responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
  • Use the timer to practice time management. You can pause, restart, or hide the timer as needed.
  • Mark for Review if you want to come back to a question later.
  • Your responses are saved automatically as you type. You can also use the drawing tool for questions that require diagrams or graphs.
  • Use the toolbar for formatting options like bold, italic, subscript, and superscript.
  • Navigate between questions using the Previous and Next buttons at the bottom of the screen.

Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.