Precalculus: Advanced Functions
Build advanced function skills for Calculus readiness: transformations, inverses, polynomials, rational functions, exponentials, logarithms, sequences, parametric and polar forms, and introductory limits.
High school, college repair, adult learners, homeschool students, and STEM-ready learners8 units58 lessons960 practice & quiz problemsFree
Not sure where to start? Take the free 15-minute placement check to pinpoint your gaps, then practice with instant feedback and worked solutions.
Take the free Precalculus placement check Open the Precalculus courseCourse outline
Function Foundations and Behavior
- What a Function Is
- Function Notation
- Domain and Range from Graphs
- Domain and Range from Equations
- Intercepts and Key Features
- Average Rate of Change
- Unit 1 Review and Quiz
Transformations and Combinations of Functions
- Vertical and Horizontal Shifts
- Reflections and Stretches
- Combining Transformations
- Even and Odd Functions
- Function Operations
- Composition of Functions
- Unit 2 Review and Quiz
Inverse Functions
- What an Inverse Function Means
- One-to-One Functions
- Horizontal Line Test
- Finding Inverses Algebraically
- Graphs of Inverse Functions
- Unit 3 Review and Quiz
Polynomial Functions
- Polynomial Vocabulary and Degree
- End Behavior
- Zeros and Multiplicity
- Graphing Polynomial Functions
- Polynomial Division
- Remainder and Factor Theorems
- Building Polynomials from Zeros
- Unit 4 Review and Quiz
- Precalculus Mid-Course Checkpoint
Rational Functions
- Rational Function Basics
- Domain Restrictions and Holes
- Vertical Asymptotes
- Horizontal and Slant Asymptotes
- Graphing Rational Functions
- Solving Rational Equations
- Unit 5 Review and Quiz
Exponential and Logarithmic Functions
- Exponential Growth
- Exponential Decay
- Transformations of Exponential Functions
- Logarithms as Inverses
- Logarithm Rules
- Solving Exponential and Logarithmic Equations
- Unit 6 Review and Quiz
Sequences, Series, and Discrete Models
- Arithmetic Sequences
- Geometric Sequences
- Recursive Formulas
- Explicit Formulas
- Sigma Notation
- Finite Series
- Unit 7 Review and Quiz
Parametric, Polar, Vectors, and Intro to Limits
- Parametric Equations
- Graphing Parametric Curves
- Polar Coordinates
- Converting Between Polar and Rectangular Form
- Vectors in the Plane
- Difference Quotients and Informal Limits
- Unit 8 Review and Quiz
- Precalculus Final Readiness Check
Frequently asked questions
Is the Precalculus course free?
Yes. The entire Precalculus course — 58 lessons, 960 practice and quiz problems, worked solutions, and the placement check — is free to use at ClearMath Academy.
What does the Precalculus course cover?
Build advanced function skills for Calculus readiness: transformations, inverses, polynomials, rational functions, exponentials, logarithms, sequences, parametric and polar forms, and introductory limits. It spans 8 units and 58 lessons, each with a worked example and practice problems with step-by-step solutions.
Who is Precalculus for?
Precalculus is aimed at high school, college repair, adult learners, homeschool students, and stem-ready learners. You can take a free 15-minute placement check first to find exactly which lessons to start with.
How do I find my gaps in Precalculus?
Take the free Precalculus placement check. It pinpoints the specific skills you're missing in about 15 minutes and builds a practice plan focused on those gaps.