About This Chapter
NMTA Essential Academic Skills Math: Continuity- Chapter Summary
As you study for calculus-related math questions on the NMTA Essential Academic Skills test, you can use this chapter as one of your major resources to help refresh your memory about the topic of continuity. Our instructors have separated this topic into several smaller lessons, allowing you to recall the different aspects of continuity in greater detail, including how to solve equations and apply related theorems. By making your way through this chapter, you will sharpen your knowledge base and be prepared to do the following:
- Describe how continuity works in a function
- Identify discontinuities in graphs and functions
- Analyze functions with regions of continuity
- Check out the Intermediate Value Theorem
You can evaluate your familiarity with continuity by using our lesson quizzes. These quizzes are connected to every lesson we offer, and they consist of about five selected-response style questions. For math-related topics, you may be asked questions about key terms, mathematical principles, true or false statements, or you may have to apply what you know to solve sample problems. Since the lesson quizzes pertain to only the information in the attached lesson, these quizzes provide a more focused assessment strategy. In addition, if you miss any questions, you will know exactly where to go in the lesson to find the right answers.
1. 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.
2. Discontinuities in Functions and Graphs
In this lesson, we talk about the types of discontinuities that you commonly see in functions. In particular, learn how to identify point, jump and asymptotic discontinuities.
3. 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.
4. 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.
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Other chapters within the College Algebra: Help and Review course
- Basic Arithmetic
- Overview of Real Numbers
- Foundations and Linear Equations: Help and Review
- Overview of Linear Equations
- Matrices and Absolute Value: Help and Review
- Inequalities: Help and Review
- Using FOIL, Graphing Parabolas & Solving Quadratics to Factor: Help & Review
- Properties of Polynomial Functions
- Working with Quadratic Equations
- Complex Numbers: Help and Review
- Exponents and Exponential Expressions
- Overview of Exponents
- Exponents and Polynomials: Help and Review
- Algebraic Expressions and Equations
- Rational Expressions: Help and Review
- Working with Rational Expressions
- Math Expressions and Formulas
- Functions: Help and Review
- Exponentials and Logarithms: Help and Review
- Probability Mechanics: Help and Review
- Calculations, Ratios & Proportions
- Percent Notation
- Data, Statistics & Probability
- Sequences and Series: Help and Review
- Basic Number Sense and Operations
- Overview of Roots & Radical Expressions
- Overview of Mathematical Limits