AP®︎ Precalculus Unit 2: Notes & Study Guide

Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 2 of AP Precalculus – Exponential and Logarithmic Functions.

Exam weight: 27-40%
15 Topics

Unit 2: Exponential and Logarithmic Functions

This unit explores exponential and logarithmic functions as inverse relationships and uses them to model growth, decay, and real-world data.

Begin with Topic 2.1: Change in Arithmetic and...

To review Unit 2, go through each of the 15 topics below.

Everything you actually need to know for your Unit 2 test, pulled directly from the AP® Precalculus curriculum.

Topic 2.1
~5 min
Review
Change in Arithmetic and Geometric Sequences
Change in Arithmetic and Geometric Sequences
  • Two patterns a sequence can follow
  • Writing the General Term
  • Finding the Change Parameter and Building the Rule
Review
Topic 2.2
~6 min
Review
Change in Linear and Exponential Functions
Change in Linear and Exponential Functions
  • Linear and Exponential Change
  • Matching Sequences to Functions
  • How to Tell Which Model Fits
Review
Topic 2.3
~6 min
Review
Exponential Functions
Exponential Functions
  • What an Exponential Function Is
  • Key Characteristics from \(a\) and \(b\)
  • Recognizing Exponential Behavior in Equations Tables and Graphs
Review
Topic 2.4
~5 min
Review
Exponential Function Manipulation
Exponential Function Manipulation
  • What Equivalent Exponential Forms Are
  • The Exponent Rules That Drive the Rewrites
  • Rewriting Exponential Functions to Show Transformations
Review
Topic 2.5
~5 min
Review
Exponential Function Context and Data Modeling
Exponential Function Context and Data Modeling
  • What an Exponential Model Means
  • Building the Model
  • Recognizing Exponential Structure in Data
Review
Topic 2.6
~7 min
Review
Competing Function Model Validation
Competing Function Model Validation
  • Linear vs quadratic vs exponential models
  • Building and comparing the candidate models
  • Residuals and what their signs mean
Review
Topic 2.7
~5 min
Review
Composition of Functions
Composition of Functions
  • Nesting one function inside another
  • Evaluating and Constructing Composites
  • Domain and Order Matter
Review
Topic 2.8
~5 min
Review
Inverse Functions
Inverse Functions
  • What an Inverse Function Is
  • When a Function Has an Inverse
  • Finding the Inverse
Review
Topic 2.9
~5 min
Review
Logarithmic Expressions
Logarithmic Expressions
  • What a Logarithm Means
  • Evaluating Logarithmic Expressions
  • Estimating and Checking Logarithm Values
Review
Topic 2.10
~5 min
Review
Inverses of Exponential Functions
Inverses of Exponential Functions
  • What Logarithmic Functions Are
  • How to Construct the Inverse
  • What the Inverse Relationship Looks Like
Review
Topic 2.11
~6 min
Review
Logarithmic Functions
Logarithmic Functions
  • What Logarithmic Functions Are
  • How the Graph Behaves
  • Asymptotes, End Behavior, and Transformed Arguments
Review
Topic 2.12
~5 min
Review
Logarithmic Function Manipulation
Logarithmic Function Manipulation
  • What Logarithm Manipulation Means
  • The Log Properties You Use to Rewrite Expressions
  • Expanding and Condensing Logarithms
Review
Topic 2.13
~5 min
Review
Exponential and Logarithmic Equations and Inequalities
Exponential and Logarithmic Equations and Inequalities
  • Solving Exponential and Logarithmic Equations
  • Restrictions and Extraneous Solutions
  • Solving Exponential and Logarithmic Inequalities
Review
Topic 2.14
~5 min
Review
Logarithmic Function Context and Data Modeling
Logarithmic Function Context and Data Modeling
  • What a Logarithmic Model Means
  • Ways to Build a Logarithmic Model
  • Using the Model to Predict and Solve
Review
Topic 2.15
~6 min
Review
Semi-log Plots
Semi-log Plots
  • Reading exponential data on a log scale
  • Recognizing When an Exponential Model Fits
  • Building the Linearization and Recovering the Exponential Model
Review

Notes

1 credit used · 5/5 remaining