About This Chapter
Functions in Math - Chapter Summary
Mathematical functions are just rules or special equations that turn one number into another. This chapter explains function notation and how vertical line testing can find out whether an equation is really a function. You can learn to compose, add, subtract, multiply, divide, evaluate, manipulate and graph functions through the lessons in this chapter.
Practice problems are included to give you plenty of experience. In addition, you can also explore polynomial, piecewise, periodic, recursive and parametric functions. Can't wait to get started? Here's a list of concepts you'll find in this chapter:
- Transformation types
- Methods for performing function translations
- Domain and range of a function
- Inverse functions and the horizontal line test
- Compounding and manipulating functions
- Factoring and simplifying polynomials
- Finding the domain, graphing and translating piecewise functions
Each lesson offers a video presentation, transcript and quiz. The helpful video tags can show you exactly where on the videos certain concepts appear. The short quizzes are multiple-choice and are useful for helping you gauge your comprehension of the material.
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 within the SAT Subject Test Mathematics Level 2: Practice and Study Guide course
- Structure & Strategies for the SAT Math Level 2
- Basic Math Review
- Square Roots
- Basic Algebraic Expressions
- Algebraic Linear Equations & Inequalities
- Algebra: Absolute Value Equations & Inequalities
- Algebra: Polynomials
- Algebra: Rational Expressions
- Understanding Sequences & Series
- Understanding Exponentials & Logarithms
- Complex and Imaginary Numbers
- Coordinate Geometry Basics
- Coordinate Geometry: Graphing Linear Equations & Inequalities
- Advanced Coordinate Geometry
- Three-Dimensional Geometry
- Overview of Trigonometry
- Probability, Combinations & Permutations
- Working with Data & Statistics
- Basic Mathematical Logic
- Limits of Functions
- SAT Subject Test Mathematics Level 2 Flashcards