# Ch 18: Functions: Help and Review

### About This Chapter

## Summary

The Functions chapter of this College Algebra Help and Review course is the simplest way to master functions. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of functions.

## Who's It For?

Anyone who needs help learning or mastering college algebra material will benefit from taking this course. There is no faster or easier way to learn college algebra. Among those who would benefit are:

- Students who have fallen behind in understanding functions or transformations
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about functions
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the functions chapter exam.

### Why it works:

**Study Efficiently:**Skip what you know, review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the functions chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any functions question. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

### Students will review:

This chapter helps students review the concepts in a functions unit of a standard college algebra course. Topics covered include:

- Function notation
- Shifting graphs on a plane
- Adding, subtracting, multiplying and dividing functions
- Composing functions
- Inverse functions
- Applying function operations

### 1. Functions: Identification, Notation & Practice Problems

A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!

### 2. Transformations: How to Shift Graphs on a Plane

What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!

### 3. What Is Domain and Range in a Function?

The domain and range are the possible outputs and inputs of a function. In this lesson, learn about what might restrict the domain and how to figure out the domain and range from a graph.

### 4. 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!

### 5. 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.

### 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.

### 7. 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!

### 8. Profit Function: Equation & Formula

This lesson will tell you how to write and use a special type of function called a profit function. After completing this lesson, you will also be able to evaluate profit functions and use them in real life scenarios.

### 9. Abstract Equation: Definition & Concept

Being able to think abstractly is a great skill to have. Learn how abstract equations can help you in refining your abstract-thinking ability. Also, learn what some of them look like and memorize their applications.

### 10. Dividing Functions: Examples & Overview

In this lesson, learn how to use long division to divide functions. Learn how the process is similar to using long division for numbers. Also learn what kinds of functions you can divide.

### 11. End Behavior in Math: Definition & Rules

All functions can be graphed. In this lesson, we will be looking at the end behavior of several basic functions. You will find that functions' leading terms indicate what kind of end behavior will be exhibited.

### 12. Partial Derivative: Definition, Rules & Examples

When a function depends on more than one variable, we can use the partial derivative to determine how that function changes with respect to one variable at a time. In this lesson, we use examples to define partial derivatives and to explain the rules for evaluating them.

### 13. Partial Differentiation: Definition, Rules & Application

In this lesson, you will be introduced to a method for finding derivatives of a multivariable function, the so-called partial derivatives. A few examples and applications will also be given.

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### Other Chapters

Other chapters within the College Algebra: Help and Review course

- Basic Arithmetic
- Overview of Real Numbers
- Foundations and Linear Equations: Help and Review
- Overview of Linear Equations
- Matrices and Absolute Value: Help and Review
- Inequalities: Help and Review
- Using FOIL, Graphing Parabolas & Solving Quadratics to Factor: Help & Review
- Properties of Polynomial Functions
- Working with Quadratic Equations
- Complex Numbers: Help and Review
- Exponents and Exponential Expressions
- Overview of Exponents
- Exponents and Polynomials: Help and Review
- Algebraic Expressions and Equations
- Rational Expressions: Help and Review
- Working with Rational Expressions
- Math Expressions and Formulas
- Fractions
- Factoring
- Exponentials and Logarithms: Help and Review
- Probability Mechanics: Help and Review
- Calculations, Ratios & Proportions
- Percent Notation
- Data, Statistics & Probability
- Sequences and Series: Help and Review
- Basic Number Sense and Operations
- Overview of Roots & Radical Expressions
- Overview of Continuity in Mathematics
- Overview of Mathematical Limits