# Ch 8: Functions in Math: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering SAT mathematics level 2 material will benefit from taking this course. There is no faster or easier way to prepare for this SAT math subject test. Among those who would benefit are:

- Students who have fallen behind in understanding how to graph the different types of functions or perform basic function operations
- 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 for the SAT exam
- 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 in Math 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 in Math 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 math course. Topics covered include:

- Function notation
- Domain and range
- Transformations
- Inverse functions
- Composite functions
- Functions of functions
- Polynomial functions
- Piecewise functions
- Periodic functions
- Recursive functions
- Parametric functions

### 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. 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.

### 8. How to Evaluate Composite Functions

Sometimes a math function depends on the outcome of another function. This lesson breaks down this chain reaction, called a composite function, and how to evaluate them.

### 9. 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!

### 10. 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!

### 11. 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.

### 12. Polynomial Functions: Properties and Factoring

Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.

### 13. Polynomial Functions: Exponentials and Simplifying

How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.

### 14. What are Piecewise Functions?

A piecewise function is a certain type of function that is made up of different parts. This lesson will define and describe piecewise functions and teach you how to identify them and how to write them.

### 15. How to Find the Domain of Piecewise Functions

The domain of any function is all the values that x can be for that function. Piecewise functions are special functions that have different parts with unique rules for each part. This lesson will show you how to find the domain for piecewise functions.

### 16. How to Graph Piecewise Functions

Piecewise functions are specific functions that have more than one piece. There is a special trick to graphing these type of functions, which you will learn in this lesson.

### 17. Translating Piecewise Functions

Piecewise functions are two or more functions that only use part of a domain. If these functions need to be changed, we can translate them without even having to know the equation.

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### Other Chapters

Other chapters within the SAT Mathematics Level 2: Help and Review course

- Basic Math Review: Help and Review
- Square Roots: Help and Review
- Basic Algebraic Expressions in Math: Help and Review
- Exponents in Math: Help and Review
- Linear Equations & Inequalities in Algebra: Help and Review
- Absolute Value Equations & Inequalities: Help and Review
- Polynomials in Algebra: Help and Review
- Rational Expressions in Algebra: Help and Review
- Matrices: Help and Review
- Sequences and Series in Math: Help and Review
- Exponentials and Logarithms in Math: Help and Review
- Complex Numbers in Math: Help and Review
- Coordinate Geometry Basics: Help and Review
- Graphing Linear Equations & Inequalities: Help and Review
- Advanced Coordinate Geometry: Help and Review
- Three-Dimensional Geometry: Help and Review
- Overview of Trigonometry: Help and Review
- Probability, Combinations & Permutations: Help and Review
- Working with Data & Statistics: Help and Review
- Logic: Help and Review
- Limits in Math: Help and Review