# Ch 28: SAT Math - Functions: Tutoring Solution

### About This Chapter

## How it works:

- Begin your review or other SAT preparation 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 prep tutoring solution will benefit any student who is trying to review functions and earn acceptable scores on the SAT. This resource can help students including those who:

- Struggle with understanding composition of functions, inverse functions, or any other functions topic
- Have limited time for studying
- Want a cost effective way to supplement their SAT math preparation
- Prefer learning SAT math topics visually
- Find themselves needing help with the functions portion of their review
- Cope with ADD or ADHD
- Want to get ahead in their SAT math preparation
- Don't have access to an SAT math instructor

## Why it works:

**Engaging Tutors:**We make reviewing functions for the SAT 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 SAT prep tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn functions 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

- Review key terms and basic function principles.
- Study function identification and notification.
- Determine domain and range in a function.
- Learn how to compose functions and add, subtract and multiply functions.
- Review methods for graphing functions and functions of functions.
- Find out how to graph the inverse function.
- Study exponential functions and polynomial functions.
- Learn to simplify polynomial functions.

### 1. What is a Function: Basics and Key Terms

Mapping numbers sounds complex, but we do it when we buy gasoline. We pump gasoline, and the gas station charges us based on the amount of gas that we pump. Learn how this relates to functions while reviewing the basics and notations in this lesson.

### 2. 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!

### 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 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.

### 5. 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!

### 6. 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!

### 7. Graphing Basic Functions

Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.

### 8. 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!

### 9. 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.

### 10. 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.

### 11. What Is an Exponential Function?

Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!

### 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.

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### Other Chapters

Other chapters within the SAT Prep: Tutoring Solution course

- SAT - About the Test: Tutoring Solution
- SAT Writing - About the Writing Section: Tutoring Solution
- SAT Writing - Word Choice & Expression: Tutoring Solution
- SAT Writing - Standard English Grammar: Tutoring Solution
- SAT Writing - Writing & Language Test Practice: Tutoring Solution
- SAT Writing - The Essay Portion: Tutoring Solution
- SAT Writing - Planning and Writing Your Essay: Tutoring Solution
- SAT Writing - Parts of an Essay: Tutoring Solution
- SAT Writing - Sentence Clarity and Structure: Tutoring Solution
- SAT Writing - Essay Writing Skills: Tutoring Solution
- SAT Writing - Grammar and Usage: Tutoring Solution
- SAT Writing - Supporting Your Writing: Tutoring Solution
- SAT Writing - Revising Your Writing: Tutoring Solution
- SAT Reading - About the Reading Section: Tutoring Solution
- SAT Reading - Sentence Completions: Tutoring Solution
- SAT Reading - Reading Passages: Tutoring Solution
- SAT Reading - Understanding Reading Passages: Tutoring Solution
- SAT Reading - Interpreting & Analyzing Text: Tutoring Solution
- SAT Reading - Literary Terms: Tutoring Solution
- SAT Reading - US Documents & Speeches: Tutoring Solution
- SAT Vocabulary Practice
- SAT Math - About the Math Section: Tutoring Solution
- SAT Math - Numbers and Operations: Tutoring Solution
- SAT Math - Exponents: Tutoring Solution
- SAT Math - Equations and Expressions: Tutoring Solution
- SAT Math - Rational Equations and Expressions: Tutoring Solution
- SAT Math - Inequalities: Tutoring Solution
- SAT Math - Quadratic Equations: Tutoring Solution
- SAT Math - Ratios, Rates & Proportional Relationships: Tutoring Solution
- SAT Math - Unit Rate & Measurement Conversions: Tutoring Solution
- SAT Math - Geometry and Measurement: Tutoring Solution
- SAT Math - Triangles & Trigonometric Rates: Tutoring Solution
- SAT Math - Data Analysis, Statistics and Probability: Tutoring Solution