About This Chapter
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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.
- Explain function basics and key terms
- Understand domain and range in functions.
- Practice the composition of functions.
- Learn to graph basic functions.
- Explore inverse, exponential and polynomials 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 within the PSAT Prep: Tutoring Solution course
- PSAT Prep - About the Test: Tutoring Solution
- PSAT Writing - About the Writing Section: Tutoring Solution
- PSAT Writing - Grammar and Usage: Tutoring Solution
- PSAT Reading - About the Reading Section: Tutoring Solution
- PSAT Reading - Sentence Completions: Tutoring Solution
- PSAT Reading - Reading Passages: Tutoring Solution
- PSAT Reading - Understanding Reading Passages: Tutoring Solution
- PSAT Reading - Literary Terms: Tutoring Solution
- PSAT Math - About the Math Section: Tutoring Solution
- PSAT Math - Numbers and Operations: Tutoring Solution
- PSAT Math - Equations and Expressions: Tutoring Solution
- PSAT Math - Exponents: Tutoring Solution
- PSAT Math - Rational Equations and Expressions: Tutoring Solution
- PSAT Math - Inequalities: Tutoring Solution
- PSAT Math - Geometry and Measurement: Tutoring Solution
- PSAT Math - Data Analysis, Statistics and Probability: Tutoring Solution