About This Chapter
Functions, Limits & Continuity - Chapter Summary
This chapter includes lessons on functions, limits, and continuity. There are discussions on topics such as defining limits using a graph, defining regions of continuity, and using exponential functions. There are also tips for solving complex problems. By the end of the chapter, you should be ready to:
- Discuss the basics of functions and understand key terms
- Plot points in the Cartesian plane
- Graph inverse functions and functions within functions
- Locate the inverse of logarithmic functions
- Solve complex problems applying different properties of functions
- Define intermediate value theorem and the mathematical notation of limits
- Identify the differences between continuous and discontinuous functions
- Explore the special properties of hyperbolic functions
We use brief lessons that help you easily understand the topics presented. Our expert instructors provide plenty of examples. For video lessons, the timelines let you easily navigate to specific topics. You can review all the lessons in order, or just the ones that cover the topics you need to review. A brief multiple-choice quiz is available for each lesson to test your knowledge.
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. 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.
3. 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!
4. 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.
5. Writing the Inverse of Logarithmic Functions
Watch this video lesson to learn how inverses are related to the original function. Also learn a method to find the inverse of logarithmic functions that you can easily use.
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. Intermediate Value Theorem: Definition
A UFO and a jet take off and ascend to 30,000 feet along discontinuous and continuous paths, respectively. In this lesson, learn about the intermediate value theorem and why the jet has to cross 15,000 feet.
8. Understanding Limits: Using Notation
Join me on a road trip as we define the mathematical notation of limits. As time goes by and I traverse hills and highways, the limit of my speed changes. Learn how to write these limits in this lesson.
9. Using a Graph to Define Limits
My mom always said I tested the limits of her patience. Use graphs to learn about limits in math. You won't get grounded as we approach limits in this lesson.
10. Continuity in a Function
Travel to space and explore the difference between continuous and discontinuous functions in this lesson. Learn how determining continuity is as easy as tracing a line.
11. Regions of Continuity in a Function
Can Earth ever compete with extraterrestrial UFOs? In this lesson, you'll learn that not all functions are continuous, but most have regions where they are continuous. Discover how to define regions of continuity for functions that have discontinuities.
12. 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!
13. Hyperbolic Functions: Properties & Applications
Although related to trigonometric functions, hyperbolic functions have special properties. In this lesson, you'll explore the properties of hyperbolic functions and their usage in both theoretical and real-world applications.
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Other chapters within the NDA Exam Preparation & Study Guide course
- About the NDA Exam
- Algebra Concepts
- Advanced Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Analytic Geometry
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Differential Equations & Applications
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Probability Concepts in Math
- Grammar and Usage
- Improving Reading Comprehension
- Measurements in Physics
- Motion in Physics
- Basics of Work, Power & Energy
- Understanding Heat Transfer
- Sound Waves
- Light, Mirrors & Lenses
- Electric Currents & Power
- Scientific Technology, Machines & Tools
- The Atom & Structure of Elements
- Chemical Properties of Elements & Substances
- Chemical Symbols, Formulas & Reactions
- Qualities of Living Organisms
- Health Science Basics
- Solar System & Eclipses
- Achievements of Famous Scientists
- Indian History
- Overview of Major World History Events
- World Government Types
- The Earth
- Earth's Oceans, Atmosphere & Climate
- Regional Geography of South Asia
- Modern Day Events in India
- NDA Exam Preparation & Study Guide Flashcards