About This Chapter
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- Begin your GRE review.
- Identify the functions concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
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This chapter of our GRE prep tutoring solution will benefit any student who is trying to prepare for the GRE and earn acceptable scores. This resource can help students including those who:
- Struggle with understanding domain, range, composition of functions or any other functions topic
- Have limited time for studying
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- Find themselves struggling with their functions review
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- Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.
- Review how to identify and write functions.
- Find out what might restrict a domain.
- Learn how to figure out domain and range from a graph.
- Practice applying the various properties of functions to solve complex problems.
- Learn to compose, add, subtract, multiply and divide functions.
- Review how to graph basic functions as well as functions of functions.
- Explore inverse functions, including how to write and graph them.
- Learn to factor polynomials and quadratics.
- Study powers, and learn to simplify math problems with exponents.
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. 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.
3. 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!
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. 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.
7. 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.
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. 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.
10. 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.
11. 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.
12. 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.
13. Concave Down: Definition, Function & Graph
In this lesson, you'll learn about regions of curves that are concave down. You'll discover the mathematics behind concave down and see how calculus is used to identify concave down regions on curves.
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