Contents of Pre Calculus

Intro to Precalculus

Introduction to Functions

How to Evaluate Functions

Finding the Domain of Functions

Operations of Functions

Using the Vertical Line Test

Features of Graphs, Domain, Range

Even vs Odd

Increasing vs Decreasing

Extrema

Average Rate of Change of a Function

How to Graph Piecewise Functions

Graphs You Must Know

Introduction to Graph Transformations

How to Graph with Transformations

Introduction to Solving Quadratics

The Square Root Method in Solving Quadratics

Using Factoring to Solve Quadratics

Completing the Square Made Easy

Proving the Quadratic Formula – Twice

Using the Quadratic Formula

Finding Intersections of Functions

Using Substitutions to Solve Equations

Graphing Quadratic Functions

Solving Quadratic Inequalities

Applications of Quadratic Functions

Introduction to Polynomial Functions

Power Functions

Multiplicity and End Behavior of Polynomials

Creating Polynomials from Real Zeros

How to Sketch Polynomial Functions

Synthetic Division and Long Division of Polynomials

Descartes Rule of Signs

How to Use the Rational Zeros Theorem

Introduction to Complex Solutions of Polynomials

Creating Polynomials from Complex Solutions

Finding ALL Solutions of Polynomials

Finding Vertical Asymptotes of Rational Functions

Graphing Rational Functions with Transformations

Finding a Horizontal Asymptote of a Rational Function

Finding an Oblique Asymptote of a Rational Function

Finding End Behavior of Rational Functions

Finding Asymptotes and Holes of Rational Functions

Graphing Rational Functions

Inequalities with Functions – Graphically

Inequalities with Polynomial Functions

Inequalities with Rational Functions

Composition of Functions

Finding Domain of Composite Functions

One to One Functions

Finding Inverse Functions

Graphs of Exponential Functions

Graphing Exponential Functions with Transformations

Solving Exponential Equations with Common Bases

Introduction to Logarithms and Their Graphs

Graphing Logarithms with Transformations

Introduction to Solving Logarithms and Exponentials

Properties of Logarithms

How to Expand Logarithms

How to Combine Logarithms

How to Change the Base of a Logarithm

Solving Logarithms with Common Bases

Solving Logarithmic Equations with Exponentials

Solving Exponential Equations with Logarithms

Review of Compound Interest

Exponential Growth and Decay

Introduction to Sequences

Introduction to Series and Summation Notation

Arithmetic Sequences

Arithmetic Series

Geometric Sequences

Geometric Series

Proof by Mathematical Induction

Introduction to Angles

Converting Degrees, Minutes, and Seconds

Introduction to Radians

Converting Radians and Degrees

Area of a Sector, Angular Velocity, Applications

Trigonometric Functions and the Unit Circle

How to Use the Unit Circle in Trigonometry

Basic Properties of Trigonometric Functions

Reciprocal Identities in Trigonometry

Pythagorean Identities for Trigonometric Functions

The Graphs of Sine and Cosine

Graphing Transformations with Sine and Cosine

How to Graph Tangent and Cotangent

Graphing Transformations with Tangent and Cotangent

How to Graph Cosecant and Secant

How to Graph Phase Shifts of Trigonometric Functions

Introduction to Inverse Trigonometric Functions

How to Use Inverse Trigonometric Functions

How to Find Inverse Trigonometric Functions

How to Solve Basic Inverse Trigonometric Functions

An In-depth Look at Using Inverse Trig Functions

How to Solve Trigonometric Equations

Introduction to Using Trigonometric Identities

How to Prove Trigonometric Identities

Introduction to Sum and Difference Formulas in Trigonometry

Using Sum and Difference Formulas in Trigonometry

Proving the Double and Half Angle Formulas for Trigonometry

How to Use the Double and Half Angle Formulas for Trigonometry

How to Use Product to Sum and Sum to Product Formulas in Trig

Introduction to Right Triangle Trigonometry

Finding Sides and Angles with Right Triangle Trigonometry

How to Use the Law of Sines in Trigonometry

How to Use the Law of Cosines in Trigonometry

How to Find the Area of a Triangle with Trigonometry

Simple Harmonic Motion in Trig

Introduction to Polar Coordinates

How to Convert From Polar Coordinates to Rectangular Coordinates

How to Convert From Rectangular Coordinates to Polar Coordinates

How to Convert From Rectangular Equations to Polar Equations

How to Convert From Polar Equations to Rectangular Equations

How to Graph Basic Polar Equations

How to Graph Advanced Polar Equations with Symmetry

Pre Calculus

Pre-calculus bridges algebra, geometry, and trigonometry with the analytical thinking required for calculus. This page guides you through foundational concepts, graphing techniques, and function analysis to prepare you for more advanced topics. Use the table of contents on the left to explore each concept in depth.

What you’ll learn

Understand and analyze different types of functions: linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric.
Work with transformations, compositions, inverses, and properties of functions.
Apply algebraic and graphical techniques to solve equations and inequalities.
Master trigonometric fundamentals, graphing, identities, and equations.
Explore sequences, series, and polar coordinates to build a strong pre-calculus foundation.