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.
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.
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
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
Exponential Functions
Exponential Functions
- What an Exponential Function Is
- Key Characteristics from \(a\) and \(b\)
- Recognizing Exponential Behavior in Equations Tables and Graphs
Exponential Function Manipulation
Exponential Function Manipulation
- What Equivalent Exponential Forms Are
- The Exponent Rules That Drive the Rewrites
- Rewriting Exponential Functions to Show Transformations
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
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
Composition of Functions
Composition of Functions
- Nesting one function inside another
- Evaluating and Constructing Composites
- Domain and Order Matter
Inverse Functions
Inverse Functions
- What an Inverse Function Is
- When a Function Has an Inverse
- Finding the Inverse
Logarithmic Expressions
Logarithmic Expressions
- What a Logarithm Means
- Evaluating Logarithmic Expressions
- Estimating and Checking Logarithm Values
Inverses of Exponential Functions
Inverses of Exponential Functions
- What Logarithmic Functions Are
- How to Construct the Inverse
- What the Inverse Relationship Looks Like
Logarithmic Functions
Logarithmic Functions
- What Logarithmic Functions Are
- How the Graph Behaves
- Asymptotes, End Behavior, and Transformed Arguments
Logarithmic Function Manipulation
Logarithmic Function Manipulation
- What Logarithm Manipulation Means
- The Log Properties You Use to Rewrite Expressions
- Expanding and Condensing Logarithms
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
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
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
Notes
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