# Ch 28: SAT Math: Functions

### About This Chapter

## SAT Math: Functions - Chapter Summary

Review the basics and key terms related to functions and then delve into the compounding and graphing of those functions. Our interesting videos are short and user-friendly. You can explore the following topics:

- Identification and notation
- Domain and range
- Composing, adding, subtracting, multiplying and dividing functions
- Graphing and compounding functions
- Inverse and exponential functions
- Factoring and simplifying polynomial functions

Complete the quick quiz at the end of each lesson to check for understanding. Target any areas that need more practice.

### SAT Math Objectives

The math section of the SAT that addresses algebra and functions composes 35-40% of the exam. The following concepts are included on the test:

- Concepts of algebraic functions
- Direct and inverse variation
- Exponent properties
- Substitution and simplification of expressions
- Word problems in algebra
- Linear equations and inequalities
- Quadratic equations
- Radical and rational equations
- Equations of lines
- Absolute value

These lessons can help you prepare for the math section of your SAT. In addition to watching the video lessons and taking the short quizzes for self-assessment, complete the exercises for extra practice in the identification, notation and application of functions.

You earn one point for each of the 58 multiple-choice math questions answered correctly. You'll find necessary formulas in your test booklet. You may use an approved model of calculator during the calculator portion of the test, although there is a section of about 20 questions on the math test where you are not allowed to use a calculator.

### 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: Practice & Study Guide course

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