About This Chapter
MTEL Math: Piecewise, Absolute Value & Step Functions - Chapter Summary
Studying for the MTEL assessment might require that you revisit math concepts you haven't explored in weeks, months or years. Get up to speed with lessons in this chapter that ensure you're prepared to do the following on the exam:
- Define piecewise functions, and find their domain
- Graph and translate piecewise functions
- Provide the meaning of the absolute value function
- Show how absolute value functions are expressed through graphs
- Share the definition of the step function, and explain how their pieces resemble steps
- Demonstrate the process of graphing step functions
This chapter's lesson instructors are skilled at presenting topics you will see on exam day in a fun and engaging manner. Enjoy the benefit of accessing these experts from the comfort of your home or on-the-go via your mobile devices.
MTEL Math: Piecewise, Absolute Value & Step Functions Chapter Objectives
In Massachusetts, educators take the MTEL Mathematics assessment to obtain teacher licensure needed to educate students in classrooms throughout the state. The computer-based test consists of 100 multiple-choice questions and 2 open-response items that are divided into six subareas. Topics in this chapter are found in the patterns, relations and algebra subarea, which constitutes about 23% of the total test. This subarea consists of all multiple-choice questions.
You can use the lessons in this chapter to brush up on your knowledge of piecewise, absolute value and step functions as you study for the test. If you need to revisit specific portions of the videos, use timelines with video tags to skip to key topics. Test your knowledge of the lessons by taking self-assessment quizzes and a chapter exam. These steps can get you closer to your goal of earning a passing score of 240 or higher on the exam.
1. 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.
2. 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.
3. 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.
4. 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.
5. Graphing Absolute Value Equations: Dilations & Reflections
Although a basic absolute value graph isn't complicated, transformations can make them sufficiently confusing! In this lesson, you'll practice different transformations of absolute value graphs.
6. Step Function: Definition, Equation & Examples
In this lesson, we'll learn what a step function is and become comfortable with this type of function. We'll examine common examples, such as the floor and ceiling functions and the heaviside function.
7. How to Graph Step Functions
In this lesson, we'll learn the definition of a step function and two of its family members: floor functions and ceiling functions. We'll then look at how to graph step functions using two real world examples.
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Other chapters within the MTEL Mathematics (09): Practice & Study Guide course
- MTEL Math: Basic Arithmetic Operations
- MTEL Math: Absolute Value & Integers
- MTEL Math: Fractions
- MTEL Math: Decimals
- MTEL Math: Percents
- MTEL Math: Rates & Ratios
- MTEL Math: Proportions
- MTEL Math: Estimation
- MTEL Math: Origins of Math
- MTEL Math: Rational & Irrational Numbers
- MTEL Math: Complex Numbers
- MTEL Math: Properties of Numbers
- MTEL Math: Exponents & Exponential Expressions
- MTEL Math: Roots & Radical Expressions
- MTEL Math: Scientific Notation
- MTEL Math: Number Theory
- MTEL Math: Number Patterns & Sequences
- MTEL Math: Number Patterns & Series
- MTEL Math: Properties of Functions
- MTEL Math: Graphing Functions
- MTEL Math: Factoring
- MTEL Math: The Coordinate Graph & Symmetry
- MTEL Math: Linear Equations
- MTEL Math: Systems of Linear Equations
- MTEL Math: Vectors, Matrices & Determinants
- MTEL Math: Introduction to Quadratics
- MTEL Math: Working with Quadratic Functions
- MTEL Math: Polynomial Functions Basics
- MTEL Math: Higher-Degree Polynomial Functions
- MTEL Math: Rational Expressions, Functions & Graphs
- MTEL Math: Exponential & Logarithmic Functions
- MTEL Math: Measurement
- MTEL Math: Perimeter & Area
- MTEL Math: Polyhedrons & Geometric Solids
- MTEL Math: Symmetry, Similarity & Congruence
- MTEL Math: Properties of Lines
- MTEL Math: Angles
- MTEL Math: Triangles
- MTEL Math: Triangle Theorems & Proofs
- MTEL Math: Similar Polygons
- MTEL Math: The Pythagorean Theorem
- MTEL Math: Quadrilaterals
- MTEL Math: Circles
- MTEL Math: Circular Arcs & Measurement
- MTEL Math: Analytic Geometry & Conic Sections
- MTEL Math: Polar Coordinates & Parameterization
- MTEL Math: Transformations
- MTEL Math: Data & Graphs
- MTEL Math: Statistics
- MTEL Math: Data Collection
- MTEL Math: Samples & Populations
- MTEL Math: Probability
- MTEL Math: Trigonometric Functions
- MTEL Math: Graphs of Trigonometric Functions
- MTEL Math: Trigonometric Identities
- MTEL Math: Applications of Trigonometry
- MTEL Math: Limits
- MTEL Math: Continuity
- MTEL Math: Rate of Change
- MTEL Math: Derivative Calculations & Rules
- MTEL Math: Graphing Derivatives & L'Hopital's Rule
- MTEL Math: Area Under the Curve & Integrals
- MTEL Math: Integration Techniques
- MTEL Math: Integration Applications
- MTEL Math: Differential Equations
- MTEL Math: Discrete & Finite Math
- MTEL Mathematics Flashcards