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  1. AP Pre Calculus
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Function Model Selection and Assumption Articulation

Alice White

Alice White

7 min read

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Study Guide Overview

This study guide covers function modeling for AP Precalculus, focusing on selecting and applying appropriate models. It reviews linear, quadratic, polynomial, and piecewise functions, including real-world examples and how to interpret them. The guide also emphasizes understanding domain and range restrictions and articulating assumptions within the model's context. Finally, it provides practice questions and tips for the exam.

#AP Pre-Calculus: Function Modeling - Your Night-Before Guide πŸš€

Hey there! Let's get you totally prepped for your exam. This guide is designed to be your quick, go-to resource, focusing on the most important stuff and making sure you feel confident and ready. Let’s dive in!

#1.13 Function Model Selection and Assumption Articulation

#What is a Function Model? πŸ”—

A function model is a mathematical representation of a real-world situation. Think of it as a simplified version of reality that helps us understand and predict outcomes. It’s all about finding the right function (linear, quadratic, etc.) that fits the data or scenario. 🌎

!famfunc1.jpg

Caption: A curved graph showing a typical function model, like the path of a ball.

Key Concept

Choosing the right function depends on the characteristics of the data and what you're trying to analyze. Linear, quadratic, and exponential functions are common choices.

#Linear Functions πŸ”—

#Basics

Linear functions are your go-to for situations with a constant rate of change. They follow the form y = mx + b, where:

  • m is the slope (rate of change)
  • b is the y-intercept (starting point)
Quick Fact

Linear functions are perfect for modeling direct variations and simple harmonic motion. 🫨

#Example: Farmer's Crops πŸ§‘β€πŸŒΎ

A farmer tracks their earnings based on acres planted:

  • Acres (x): 0, 10, 20, 30, 40
  • Earnings (y): 0, 800, 1600, 2400, $3200

To create a linear model:

  1. Find the slope (m): Using points (0, 0) and (10, 800): m=800βˆ’010βˆ’0=80m = \frac{800 - 0}{10 - 0} = 80m=10βˆ’0800βˆ’0​=80
  2. Find the y-intercept (b): In this case, it's 0 since the line passes through the origin.

So, the model is y = 80x. If the farmer plants 50 acres, the model predicts earnings of y = 80(50) = $4,000. πŸ’°

#Quadratic Functions πŸ”—

#Basics

Quadratic functions are used for situations with a changing rate of change or when you see a symmetrical shape w...

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Question 1 of 9

A taxi charges a flat fee of 3 plus 2 for every mile driven. Which type of function best models the total cost?

Linear

Quadratic

Exponential

Piecewise