**Precalculus**

The comprehensive contents from this book, combined with Odigia’s Teaching and Learning Tools have everything you need to engage, collaborate, track and assess your students.

**This course includes:**

**326**

### practice questions

**74**

### engagement activities

**Helping Teachers Do What They Do Best: Teach**

**Customize**

Use our courses as is or easily customize them to fit your teaching style and the needs of your students. Hide and show existing content, assessments and add your own favorite resources. Everything your students need, in one place!

**Engage and Collaborate**

Odigia combines learning materials, discussions, and tools to create a familiar social experience for students allowing you to easily connect and redirect students attention.

**Track**

See how much time students are spending on different areas of the course, which areas are creating the most amount of engagement and identify topics the students are struggling with. Flag and provide feedback on assignments to proactively meet individual students' needs.

**Assess**

Game theory allows students to monitor their progress visually and motivates them to stay on track. Students can see exactly what activities they need to complete, which ones have been flagged and compare their progress against the overall class.

### Precalculus Course Outline

### What are functions?

Concepts Covered:

- How are function notation applied in functions?
- What is the difference between domain and range?
- How does the rate of change affect the behavior of graphs?
- How do you find the composition of functions?
- How can functions be transformed?
- How do you find absolute value functions?
- What are inverse functions?

### What are linear functions?

Concepts Covered:

- How do we use linear functions?
- How do we graph linear functions?
- How do we model linear functions?
- How do we fit linear models to data?

### How are polynomials related to rational functions?

Concepts Covered:

- How do we use complex numbers?
- How are quadratic functions applied in parabolas?
- What is the difference between power functions and polynomial functions?
- Why do we graph polynomial functions?
- How do we divide polynomials?
- How do we find zeros in polynomial functions?
- Why are rational functions important?
- What is the difference between inverses and radical functions?
- How do we model using variations?

### What are exponential and logarithmic functions?

Concepts Covered:

- How are exponential functions used?
- How do we graph exponential functions?
- How do we find logarithmic functions?
- How do we graph logarithmic functions?
- What are logarithmic properties?
- What is the difference between exponential and logarithmic equations?
- How do we use data to fit exponential models?
- How do we use exponential and logarithmic models?

### What are some types of trigonometric functions?

Concepts Covered:

- How are angles used in precalculus?
- What is a unit circle?
- What are some other trigonometric functions?
- How do we use right triangles in trigonometry?

### What are periodic functions?

Concepts Covered:

- How do you make graphs with sine and cosine functions?
- How do you make graphs with other trigonometric functions?
- What are inverse trigonometric functions?

### How do trigonometric identities affect equations?

Concepts Covered:

- How do we solve trigonometric equations with identities?
- How do we compare sum and difference identities?
- How do we differentiate double-angle, half-angle, and reduction formula identities?
- What is the difference between sum-to-product and product-to-sum formulas?
- How do we solve trigonometric equations?
- How do we model with trigonometric equations?

### What else is there in trigonometry?

Concepts Covered:

- How do non-right triangles relate to the law of sines?
- How do non-right triangles relate to the law of cosines?
- How are polar coordinates used?
- How are polar coordinates graphed?
- What is the polar form of complex numbers?
- How are parametric equations formed?
- How are parametric equations graphed?
- What are vectors?

### How do the systems of equations and inequalities operate?

Concepts Covered:

- How do you use the systems of linear equations using two variables?
- How do you use the systems of linear equations using three variables?
- What are the two variables in the systems of nonlinear equations and inequalities?
- Why do we get partial fractions?
- What is the difference between the matrices and matrix operations?
- How do we solve different systems with the Gaussian elimination?
- How do we solve different systems with inverses?
- How do we solve different systems using Cramer’s rule?

### What is analytic geometry?

Concepts Covered:

- How is an ellipse formed?
- What is a hyperbola?
- How do we form parabolas?
- What are the rotation of axes?
- Where are the conic sections in the polar coordinates?

### How do sequences, probability, and counting theory relate to each other?

Concepts Covered:

- How do we find sequences and their notations?
- How do we find arithmetic sequences?
- How do we find geometric sequences?
- How do we find series and their notations?
- How do we count problems with principles?
- What is binomial theorem?
- What is probability?

### Why is calculus important?

Concepts Covered:

- How do we find limits in a numerical and graphical approach?
- What are the properties of finding limits?
- How do we determine continuity?
- How do we find derivatives?

Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives and includes worked examples that demonstrate problem-solving approaches in an accessible way.

**About the authors:**

## Senior Contributing Authors

**Jay Abramson,** Arizona State Universityty

## Contributing Authors

Valeree Falduto, Palm Beach State College

Rachael Gross, Towson University

David Lippman, Pierce College

Melonie Rasmussen, Pierce College

Rick Norwood, East Tennessee State University

Nicholas Belloit, Florida State College at Jacksonville

Jean-Marie Magnier, Springfield Technical Community College

Christina Fernandez

Harold Whipple, Formerly of Columbia College