Ch 11: Understanding Function Operations: Tutoring Solution

About This Chapter

The Understanding Function Operations chapter of this High School Precalculus Tutoring Solution is a flexible and affordable path to learning about function operations. These simple and fun video lessons are each about five minutes long and they teach all of the strategies involving function operations required in a typical high school precalculus course.

How it works:

  • Begin your assignment or other precalculus 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 precalculus tutoring solution will benefit any student who is trying to learn function operations and earn better grades. This resource can help students including those who:

  • Struggle with understanding compounding functions, domain and range of composite functions, inverse 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 understanding function operations unit
  • Cope with ADD or ADHD
  • Want to get ahead in precalculus
  • Don't have access to their math teacher outside of class

Why it works:

  • Engaging Tutors: We make learning 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 precalculus tutor, these video lessons are thoroughly reviewed.
  • Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn function operations on the go!
  • Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.

Learning Objectives

  • Learn how to add, subtract, multiply and divide functions.
  • Find out how to compose functions.
  • Understand compounding functions.
  • Graph functions of functions.
  • Study how the domain and range of one function affects the domain and range of another function.
  • Learn how to find an inverse function and graph it.
  • Identify one-to-one functions algebraically and graphically.
  • Determine how to solve equations for different variables.

10 Lessons in Chapter 11: Understanding Function Operations: Tutoring Solution
Test your knowledge with a 30-question chapter practice test
How to Add, Subtract, Multiply and Divide Functions

1. How to Add, Subtract, Multiply and Divide Functions

Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!

How to Compose Functions

2. 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.

Applying Function Operations Practice Problems

3. 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!

Compounding Functions and Graphing Functions of Functions

4. 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!

Domain & Range of Composite Functions: Definition & Examples

5. 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.

Inverse Functions

6. 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.

Understanding and Graphing the Inverse Function

7. 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.

One-to-One Functions: Definitions and Examples

8. 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.

Manipulating Functions and Solving Equations for Different Variables

9. 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.

Derivative of a Function: Definition & Example

10. Derivative of a Function: Definition & Example

There are two ways to define and many ways to find the derivative of a function. In this lesson, we will define the derivative using the instantaneous rate of change and provide examples.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

Other chapters within the High School Precalculus: Tutoring Solution course

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