AP®︎ Precalculus: Topic 1.13 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 1.13 of AP Precalculus – Function Model Selection and Assumption Articulation.

Questions List

Topic 1.13

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Question 1 Easy

xx01234
f(x)f(x)221814106


Which statement identifies the best function type for the data and gives sufficient evidence for that choice?

AQuadratic, because the second differences are all 00, which is constant.
BQuadratic, because the first differences are all −4-4 over equal input intervals.
CLinear, because the first differences are all −4-4 over equal input intervals.
DLinear, because the output values decrease over each successive input interval.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 1.13: Function Model Selection and Assumption Articulation

Learning Objective: 1.13.A

Identify an appropriate function type to construct a function model for a given scenario.

Essential Knowledge: 1.13.A.1

Linear functions model data sets or aspects of contextual scenarios that demonstrate roughly constant rates of change.

Essential Knowledge: 1.13.A.2

Quadratic functions model data sets or aspects of contextual scenarios that demonstrate roughly linear rates of change, or data sets that are roughly symmetric with a unique maximum or minimum value.

Essential Knowledge: 1.13.A.3

Geometric contexts involving area or two dimensions can often be modeled by quadratic functions. Geometric contexts involving volume or three dimensions can often be modeled by cubic functions.

Essential Knowledge: 1.13.A.4

Polynomial functions model data sets or contextual scenarios with multiple real zeros or multiple maxima or minima.

Essential Knowledge: 1.13.A.5

A polynomial function of degree nn models data sets or contextual scenarios that demonstrate roughly constant nonzero nnth differences.

Essential Knowledge: 1.13.A.6

A polynomial function of degree nn or less can be used to model a graph of n+1n + 1 points with distinct input values.

Essential Knowledge: 1.13.A.7

A piecewise-defined function consists of a set of functions defined over nonoverlapping domain intervals and is useful for modeling a data set or contextual scenario that demonstrates different characteristics over different intervals.

Learning Objective: 1.13.B

Describe assumptions and restrictions related to building a function model.

Essential Knowledge: 1.13.B.1

A model may have underlying assumptions about what is consistent in the model.

Essential Knowledge: 1.13.B.2

A model may have underlying assumptions about how quantities change together.

Essential Knowledge: 1.13.B.3

A model may require domain restrictions based on mathematical clues, contextual clues, or extreme values in the data set.

Essential Knowledge: 1.13.B.4

A model may require range restrictions, such as rounding values, based on mathematical clues, contextual clues, or extreme values in the data set.

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