Variables and CoVariation - See Unit 1 PDF

Comparing Lines and Exponentials - See Unit 2 PDF

Functions - See Unit 3 PDF

Building New Functions - See Unit 4 PDF

Exponential Functions Revisited - See Unit 5 PDF

Rational Functions - See Unit 6 PDF

Analyzing Functions

Composition of Functions

Famous Functions, Updated

Composition of Functions

We explore how when can combine two functions by composing them. That is, how we can plug one function into another to create a new function.

Domains and Ranges of Composite Functions

We explore the domain and range of a composite function.

What are the Zeros of Functions?

Zeros of Functions

We explore what it means to find the zero of a function.

The Importance of the Equals Sign

We explore the similarities and differences between expressions, equations, and functions. We also look at when it is and is not appropriate to use the equals sign.

Finding Zeros

We explore what it means to find the zero of a function.

Function Transformations

Function Transformations Revisited

Solving Inequalities

Solving Inequalities Graphically

Solving Inequalities without a Graph

Origins of Trig

Right Triangle Trig

Sine, Cosine, and Tangent

Secant, Cosecant and Cotangent

All From One, One From All

The Unit Circle

Unit Circle

Trig Identities

Trigonometric Identities

Application of Trig Identities

Trigonometric Functions

The Unit Circle to the Function Graph

Traversing A Circle

The Sine and Cosine Functions

Creating a New Function: Tangent

Graphs of Secant, Cosecant, and Cotangent

In this section, we explore the graphs of secant, cosecant, and cotangent.

Trig Functions As Functions

Finding All Solutions to Trig Equations

Trig Functions as Functions

Transformations of Trig Functions

Trig Function Transformations

Some Applications of Trigonometry

Applications of Trigonometry

Inverse Functions In Depth

Review of Inverse Functions

Review of Inverse Functions

Finding Inverses Algebraically

Graphs of Inverse Functions

Logarithms

Definition of Logarithms

Properties of Logarithms

Solving Logarithmic Equations

Inverse Trigonometric Functions

Inverse Cosine

Other Inverse Trig Functions

Applications of Inverse Trigonometry

Preparing for Calculus

Linear Systems of Equations

From Systems to Solutions

Solving Systems of Equations Algebraically

This section explores using an algebraic approach to solving a system of linear equations.

Applications of Systems of Equations

This sections looks at applications of systems of equations more closely.

Non-linear Systems

Famous Formulas

Solving Non-linear Systems Graphically

Eliminating Variables

Applications of Systems

Applications of Systems

Average Rate of Change: Difference Quotients

Average Rate of Change and Secant Lines

Slopes of Secant Lines as a Function of h

Algebra of Secant Lines

Functions: The Big Picture

Functions: A Summary

What is Calculus?

Back Matter


You can download a Certificate as a record of your successes.