# Ch 12: Understanding Function Operations in Trigonometry: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other high school trigonometry work.
- Identify the function operations concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our High School Trigonometry Tutoring Solution will benefit any student who is trying to learn about function operations and earn better grades. This resource can help students, including those who:

- Struggle with understanding basic function operations, composite functions or any other function operations topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their function operations unit
- Cope with ADD or ADHD
- Want to get ahead in high school trigonometry
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors**: We make learning about function operations simple and fun.**Cost Efficient**: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality**: Unlike a live trigonometry tutor, these video lessons are thoroughly reviewed.**Convenient**: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about function operations on the go!**Learn at Your Pace**: You can pause and re-watch lessons as often as you'd like, until you master the material.

## Learning objectives:

- Learn how to compose functions
- Find out how to apply different properties of functions to solve complex problems
- Explore functions within functions
- See what makes a function a composite function
- Learn how to write, find and graph inverse functions
- Discover what makes a one-to-one function different from a regular function
- See how functions can be manipulated to solve for different variables

### 1. How to Compose Functions

Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.

### 2. Applying Function Operations Practice Problems

In this lesson, learn how to apply all the different properties of functions to solve complex problems. From function operations and composition to domain and range, get your practice here!

### 3. Compounding Functions and Graphing Functions of Functions

We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!

### 4. Domain & Range of Composite Functions: Definition & Examples

Learn what makes a function a composite function and also learn how the parts of a composite function determine its domain. Also in this video lesson, learn about the range of composite functions.

### 5. Inverse Functions

Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.

### 6. Understanding and Graphing the Inverse Function

If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.

### 7. One-to-One Functions: Definitions and Examples

Watch this video lesson to learn what makes a one-to-one function different from a regular function. Learn a simple test you can use to check whether a function is one-to-one or not.

### 8. Manipulating Functions and Solving Equations for Different Variables

Functions can be manipulated to solve for many different variables. There are certain rules to follow, but if the rules are adhered to, solving equations can be quite simple. This lesson will show you how.

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### Other Chapters

Other chapters within the High School Trigonometry: Tutoring Solution course

- Real Numbers - Types and Properties: Tutoring Solution
- Working with Linear Equations in Trigonometry: Tutoring Solution
- Working with Inequalities in Trigonometry: Tutoring Solution
- Absolute Value Equations in Trigonometry: Tutoring Solution
- Working with Complex Numbers in Trigonometry: Tutoring Solution
- Systems of Linear Equations in Trigonometry: Tutoring Solution
- Mathematical Modeling in Trigonometry: Tutoring Solution
- Introduction to Quadratics in Trigonometry: Tutoring Solution
- Working with Quadratic Functions in Trigonometry: Tutoring Solution
- Coordinate Geometry Review: Tutoring Solution
- Functions for Trigonometry: Tutoring Solution
- Graph Symmetry in Trigonometry: Tutoring Solution
- Graphing with Functions in Trigonometry: Tutoring Solution
- Basic Polynomial Functions in Trigonometry: Tutoring Solution
- Higher-Degree Polynomial Functions in Trigonometry: Tutoring Solution
- Rational Functions in Trigonometry: Tutoring Solution
- Rational Expressions & Function Graphs in Trigonometry: Tutoring Solution
- Exponential & Logarithmic Functions in Trigonometry: Tutoring Solution
- Trigonometric Functions: Tutoring Solution
- Geometry in Trigonometry: Tutoring Solution
- Triangle Trigonometry: Tutoring Solution
- Working with Trigonometric Graphs: Tutoring Solution
- Trigonometric Equations: Tutoring Solution
- Working with Trigonometric Identities: Tutoring Solution
- Applications of Trigonometry: Tutoring Solution
- Analytic Geometry & Conic Sections in Trigonometry: Tutoring Solution
- Vectors, Matrices & Determinants in Trigonometry: Tutoring Solution
- Polar Coordinates & Parameterizations: Tutoring Solution
- Circular Arcs, Circles & Angles: Tutoring Solution