# Ch 10: Functions in Math: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other SAT math work.
- Identify the functions 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 SAT Mathematics Level 2 Tutoring Solution will benefit any student who is trying to learn about functions to prepare for the subject test. This resource can help students, including those who:

- Struggle with understanding function notation, transformations, inverse functions, piecewise functions or any other functions 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 functions unit
- Cope with ADD or ADHD
- Want to excel on the SAT Mathematics Level 2 subject test
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors**: We make learning about functions 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 math tutor, these video lessons are thoroughly reviewed.**Convenient**: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about functions 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

- Review function identification and notation.
- Learn how to shift graphs on a plane.
- Study domain and range in a function.
- Find out how to add, subtract, multiply and divide functions.
- Learn how to compose functions and graph inverse functions.
- Describe methods for compounding functions and graphing functions of functions.
- Identify the properties of polynomial functions and learn how to simplify them.
- Review methods for finding the domain of piecewise functions.
- Graph and translate piecewise functions.
- Learn about periodic, recursive and 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.

### 18. Recognizing & Modeling Periodic Functions

Trigonometric functions such as sine and cosine are periodic in nature, exhibiting repeating waves through a given period. These functions serve to model physical phenomena such as sound waves and / or uniform circular motion.

### 19. Recursive Functions: Definition & Examples

After reading this lesson, you'll know how to identify recursive functions and how they work. You'll learn how to figure out the terms of these recursive functions, and you'll learn about a famous recursive function.

### 20. Recursive Sequence: Formula & Overview

One of the most famous recursive sequences is the Fibonacci sequence. In this lesson, learn what makes the Fibonacci sequence a recursive sequence, and discover how you can recognize and create your own.

### 21. Evaluating Parametric Equations: Process & Examples

After watching this video lesson, you will be able to evaluate a parametric equation for any given parameter. Learn the steps involved and what the complete answer looks like.

### 22. Converting Between Parametric & Rectangular Forms

There are all kinds of ways of writing equations. Learn about parametric equations in this video lesson. Learn how you can convert between parametric equations and their equivalent rectangular equations.

### 23. Graphs of Parametric Equations

Watch this video lesson to learn how you can go about graphing parametric equations. Learn the simplest way to graph parametric equations by eliminating the parameter.

### 24. Parametric Equations in Applied Contexts

Watch this video lesson to learn how you can use parametric equations to help you solve real world problems such as the path of a moving object. Learn how to form parametric equations to model the real world.

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### Other Chapters

Other chapters within the SAT Subject Test Mathematics Level 2: Tutoring Solution course

- SAT Math Level 2 Structure & Strategy: Tutoring Solution
- Basic Math Review: Tutoring Solution
- Square Roots: Tutoring Solution
- Basic Algebraic Expressions in Math: Tutoring Solution
- Exponents in Math: Tutoring Solution
- Vectors: Tutoring Solution
- Linear Equations & Inequalities in Algebra: Tutoring Solution
- Absolute Value Equations & Inequalities: Tutoring Solution
- Polynomials in Algebra: Tutoring Solution
- Rational Expressions in Algebra: Tutoring Solution
- Matrices: Tutoring Solution
- Sequences and Series in Math: Tutoring Solution
- Exponentials and Logarithms in Math: Tutoring Solution
- Complex Numbers in Math: Tutoring Solution
- Coordinate Geometry Basics: Tutoring Solution
- Graphing Linear Equations & Inequalities: Tutoring Solution
- Advanced Coordinate Geometry: Tutoring Solution
- Three-Dimensional Geometry: Tutoring Solution
- Overview of Trigonometry: Tutoring Solution
- Probability, Combinations & Permutations: Tutoring Solution
- Working with Data & Statistics: Tutoring Solution
- Logic: Tutoring Solution
- Limits in Math: Tutoring Solution